Metrics for Lanczos kernel

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze20.0ms (0.1%)

Memory

11.6MiB live, 50.1MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 37 to 21 computations (43.2% saved)

sample2.3s (17.6%)

Memory

49.3MiB live, 2 005.7MiB allocated

Samples

2.0s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-<=: 450.0ms (26.3% of total)

ival-sin: 446.0ms (26.1% of total)

const: 334.0ms (19.5% of total)

ival-div: 237.0ms (13.9% of total)

ival-mult: 147.0ms (8.6% of total)

ival-pi: 64.0ms (3.7% of total)

ival-and: 21.0ms (1.2% of total)

exact: 8.0ms (0.5% of total)

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

Bogosity

explain142.0ms (1.1%)

Memory

-12.6MiB live, 377.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
1	-	1	(0.47174951434135437 4.150589942932129)	`(sin.f32 (.f32 (.f32 x (PI.f32)) tau))`
0	-	0	-	`(PI.f32)`
0	-	0	-	`(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))`
0	-	0	-	`(.f32 (.f32 x (PI.f32)) tau)`
0	-	0	-	`(*.f32 x (PI.f32))`
0	-	0	-	`(sin.f32 (*.f32 x (PI.f32)))`
0	-	0	-	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
0	-	0	-	`tau`
0	-	0	-	`(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))`
0	-	0	-	`x`

Confusion

	Predicted +	Predicted -
+	0	2
-	0	254

Precision

0/0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	2
-	0	0	254

Precision?

0/0

Recall?

0.0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0.0

Samples

48.0ms

512×

valid

Compiler

Compiled 151 to 34 computations (77.5% saved)

Precisions

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

ival-sin: 16.0ms (46.5% of total)

ival-mult: 9.0ms (26.2% of total)

ival-div: 6.0ms (17.4% of total)

ival-pi: 3.0ms (8.7% of total)

ival-true: 1.0ms (2.9% of total)

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

preprocess92.0ms (0.7%)

Memory

-24.4MiB live, 103.9MiB 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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.9MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify55.0ms (0.4%)

Memory

-7.2MiB live, 32.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize41.0ms (0.3%)

Memory

-4.0MiB live, 114.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.31695921235078556	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.3359375	(*.f32 x (PI.f32))
accuracy	0.3756637695368841	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.4271087890737681	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))

Samples

31.0ms

256×

valid

Compiler

Compiled 64 to 12 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sin: 7.0ms (37.8% of total)

ival-div: 4.0ms (21.6% of total)

ival-mult: 4.0ms (21.6% of total)

ival-pi: 3.0ms (16.2% of total)

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

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

series30.0ms (0.2%)

Memory

11.7MiB live, 89.1MiB allocated

Counts

6 → 120

Calls

Call 1

Inputs
#<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))))>
#<alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))>
#<alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau))>
#<alt (.f32 (.f32 x (PI.f32)) tau)>
#<alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))>
#<alt (*.f32 x (PI.f32))>

Outputs
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))>
#<alt (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4)))))))>
#<alt (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (pow (PI) 6)))) (* 1/120 (* (pow x 4) (pow (PI) 4))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))>
#<alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))>
#<alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt 1>
#<alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))>
#<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))))))))))>
#<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))))))))))))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))>
#<alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 4)))))))>
#<alt (+ 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))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* x (+ (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 3)))) (* tau (PI))))>
#<alt (* 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))))))))>
#<alt (* 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)))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt 1>
#<alt (+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))>
#<alt (+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4))))))>
#<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)))))))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	x	@	-inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
5.0ms	tau	@	-inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
5.0ms	tau	@	inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
4.0ms	x	@	inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
3.0ms	x	@	0	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))

simplify445.0ms (3.4%)

Memory

-5.5MiB live, 578.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	1582
1	620	1562
2	2407	1538
3	4137	1538
4	4871	1538
5	5550	1538
6	5940	1538
7	5971	1538
8	5971	1538
0	8816	1486

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

rewrite197.0ms (1.5%)

Memory

30.0MiB live, 308.4MiB allocated

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

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

Counts

6 → 670

Calls

Call 1

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

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

eval95.0ms (0.7%)

Memory: -12.6MiB live, 186.1MiB allocated
Compiler: Compiled 24 386 to 2 296 computations (90.6% saved)

prune188.0ms (1.4%)

Memory

11.1MiB live, 403.4MiB allocated

Pruning

39 alts after pruning (39 fresh and 0 done)

	Pruned	Kept	Total
New	974	39	1 013
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	975	39	1 014

Accuracy

99.8%

Counts

1 014 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.9%	(/.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))
	69.9%	(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))
	97.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) (neg.f32 (*.f32 x (PI.f32)))))
	97.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))) x)
	97.4%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	97.3%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))))
▶	97.2%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)))
	97.8%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (.f32 x (PI.f32)))) (neg.f32 (sin.f32 (*.f32 x (PI.f32)))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (neg.f32 tau)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (.f32 x (PI.f32)))))
	97.3%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)))
	97.1%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) tau)) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))) x))
	97.1%	(.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))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (.f32 tau (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 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
▶	97.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (*.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 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (.f32 x (sqrt.f32 (PI.f32)))))) (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
	95.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal -1/3 binary32))))
	83.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (*.f32 x x)) #s(literal 1 binary32))))
	93.9%	(.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 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32)) (.f32 (.f32 x x) (fma.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 (.f32 x x) (*.f32 #s(literal -1/5040 binary32) (pow.f32 (PI.f32) #s(literal 6 binary32))))))) #s(literal 1 binary32))))
	68.7%	(.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)))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (PI.f32)) (.f32 (.f32 tau (sqrt.f32 (PI.f32))) x))) (/.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))))
	97.5%	(.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)))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (.f32 (PI.f32) (neg.f32 tau))))
	97.2%	(.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)))))))
▶	97.8%	(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	76.1%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau tau) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (.f32 x x))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	92.4%	(exp.f32 (.f32 (log.f32 (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))) #s(literal -1 binary32)))
	75.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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)))
	96.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau))))
	61.7%	#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))))
▶	60.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 954 to 1 056 computations (46% saved)

simplify140.0ms (1.1%)

Memory

-10.0MiB live, 229.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
cost-diff	0	(/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)))
cost-diff	384	(/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x))
cost-diff	0	(sin.f32 (*.f32 x (PI.f32)))
cost-diff	0	(neg.f32 (sin.f32 (*.f32 x (PI.f32))))
cost-diff	128	(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
cost-diff	192	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x 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))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
cost-diff	0	(.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))))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
cost-diff	0	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
cost-diff	0	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
cost-diff	704	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))

Rules

4 138×	`lower-*.f64`
4 120×	`lower-*.f32`
2 976×	`lower-/.f64`
2 954×	`lower-/.f32`
1 764×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	369
0	69	349
1	143	349
2	461	349
3	2805	349
4	5795	349
0	8251	349

Stop Event

1×	iter limit
1×	node limit
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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (PI.f32)))
(sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(literal 1 binary32)
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.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
(.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(neg.f32 (sin.f32 (*.f32 x (PI.f32))))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
x
(PI.f32)
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32)))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(*.f32 x tau)
tau
(neg.f32 (.f32 (PI.f32) (.f32 x tau)))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)))
#s(literal 1 binary32)
(/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x))
(/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(PI.f32)
(.f32 (PI.f32) (.f32 x tau))
(*.f32 x tau)
x
tau
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) x)
(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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.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 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))
(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
(.f32 (.f32 x (PI.f32)) tau)
(.f32 x (.f32 (PI.f32) tau))
(*.f32 x (PI.f32))
x
(PI.f32)
tau
(/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))))
(sin.f32 (*.f32 x (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))
(*.f32 x (PI.f32))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(literal 1 binary32)
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
(.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 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(/.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) (.f32 x tau)))
(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
(.f32 (PI.f32) (.f32 x tau))
(.f32 x (.f32 (PI.f32) tau))
(PI.f32)
(*.f32 x tau)
x
tau
(.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
(.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x 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))))))
(neg.f32 (sin.f32 (*.f32 x (PI.f32))))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
x
(PI.f32)
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau))))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 tau (neg.f32 (PI.f32)))))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (*.f32 x (PI.f32)))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
(.f32 (PI.f32) (.f32 x tau))
(.f32 x (.f32 (PI.f32) tau))
(*.f32 x tau)
tau
(neg.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 x (.f32 tau (neg.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (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))))))
#s(literal 1 binary32)
(/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x))
(/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
(PI.f32)
(.f32 (PI.f32) (.f32 x tau))
(.f32 x (.f32 (PI.f32) tau))
(*.f32 x tau)
x
tau
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) x)
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))

localize145.0ms (1.1%)

Memory

2.1MiB live, 243.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.36328125	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.36947250976844204	(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
accuracy	0.39453125	(/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
accuracy	0.40625	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)))
accuracy	0.35775375976844204	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau))))
accuracy	0.36328125	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.38509750976844204	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32)))
accuracy	0.41634750976844204	(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
accuracy	0.36166000976844204	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
accuracy	0.36328125	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.36947250976844204	(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
accuracy	0.41634750976844204	(.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))))
accuracy	12.512651652510256	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
accuracy	0.31695921235078556	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.3359375	(*.f32 x (PI.f32))
accuracy	0.3756637695368841	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.4271087890737681	(/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (PI.f32)))

Samples

82.0ms

256×

valid

Compiler

Compiled 369 to 34 computations (90.8% saved)

Precisions

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

ival-sin: 30.0ms (46.2% of total)

ival-div: 17.0ms (26.2% of total)

ival-mult: 14.0ms (21.6% of total)

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

ival-pi: 1.0ms (1.5% of total)

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

exact: 0.0ms (0% of total)

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

series54.0ms (0.4%)

Memory

-7.2MiB live, 104.1MiB allocated

Counts

20 → 420

Calls

Call 1

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

Outputs
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))>
#<alt (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4)))))))>
#<alt (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (pow (PI) 6)))) (* 1/120 (* (pow x 4) (pow (PI) 4))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))>
#<alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))>
#<alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (/ 1 (* x (PI)))>
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#<alt (+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (pow (PI) 5)))) (* 1/120 (* (pow x 3) (pow (PI) 3))))))) (/ 1 (* x (PI))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))>
#<alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))>
#<alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))>
#<alt (* tau (* x (PI)))>
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#<alt (- (* (pow tau 2) (+ (* 1/6 (* x (PI))) (* (pow tau 2) (+ (* -1/120 (* (pow x 3) (pow (PI) 3))) (* 1/5040 (* (pow tau 2) (* (pow x 5) (pow (PI) 5)))))))) (/ 1 (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (/ (* x (PI)) (sin (* x (PI))))>
#<alt (+ (* 1/6 (/ (* (pow tau 2) (* (pow x 3) (pow (PI) 3))) (sin (* x (PI))))) (/ (* x (PI)) (sin (* x (PI)))))>
#<alt (+ (* (pow tau 2) (- (* -1 (* (pow tau 2) (+ (* -1/36 (/ (* (pow x 5) (pow (PI) 5)) (sin (* x (PI))))) (* 1/120 (/ (* (pow x 5) (pow (PI) 5)) (sin (* x (PI)))))))) (* -1/6 (/ (* (pow x 3) (pow (PI) 3)) (sin (* x (PI))))))) (/ (* x (PI)) (sin (* x (PI)))))>
#<alt (+ (* (pow tau 2) (- (* (pow tau 2) (- (* -1 (* (pow tau 2) (+ (* -1/5040 (/ (* (pow x 7) (pow (PI) 7)) (sin (* x (PI))))) (+ (* 1/720 (/ (* (pow x 7) (pow (PI) 7)) (sin (* x (PI))))) (* 1/6 (* (pow x 2) (* (pow (PI) 2) (+ (* -1/36 (/ (* (pow x 5) (pow (PI) 5)) (sin (* x (PI))))) (* 1/120 (/ (* (pow x 5) (pow (PI) 5)) (sin (* x (PI))))))))))))) (+ (* -1/36 (/ (* (pow x 5) (pow (PI) 5)) (sin (* x (PI))))) (* 1/120 (/ (* (pow x 5) (pow (PI) 5)) (sin (* x (PI)))))))) (* -1/6 (/ (* (pow x 3) (pow (PI) 3)) (sin (* x (PI))))))) (/ (* x (PI)) (sin (* x (PI)))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (PI)>
#<alt (+ (PI) (* 1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 3)))))>
#<alt (+ (PI) (* (pow tau 2) (- (* -1 (* (pow tau 2) (+ (* -1/36 (* (pow x 4) (pow (PI) 5))) (* 1/120 (* (pow x 4) (pow (PI) 5)))))) (* -1/6 (* (pow x 2) (pow (PI) 3))))))>
#<alt (+ (PI) (* (pow tau 2) (- (* (pow tau 2) (- (* -1 (* (pow tau 2) (+ (* -1/5040 (* (pow x 6) (pow (PI) 7))) (+ (* 1/720 (* (pow x 6) (pow (PI) 7))) (* 1/6 (* (pow x 2) (* (pow (PI) 2) (+ (* -1/36 (* (pow x 4) (pow (PI) 5))) (* 1/120 (* (pow x 4) (pow (PI) 5))))))))))) (+ (* -1/36 (* (pow x 4) (pow (PI) 5))) (* 1/120 (* (pow x 4) (pow (PI) 5)))))) (* -1/6 (* (pow x 2) (pow (PI) 3))))))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt tau>
#<alt (* tau (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))))>
#<alt (* tau (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4))))))))>
#<alt (* tau (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (pow (PI) 6)))) (* 1/120 (* (pow x 4) (pow (PI) 4)))))))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
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#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
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#<alt (sin (* tau (* x (PI))))>
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#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
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#<alt (sin (* tau (* x (PI))))>
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#<alt (* tau (* x (PI)))>
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#<alt (* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))>
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#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* tau (* (pow x 2) (pow (PI) 2))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))))>
#<alt (/ (* tau (* (pow x 2) (pow (PI) 2))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))))>
#<alt (/ (* tau (* (pow x 2) (pow (PI) 2))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))))>
#<alt (/ (* tau (* (pow x 2) (pow (PI) 2))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
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#<alt (/ (* tau (* x (pow (PI) 2))) (sin (* tau (* x (PI)))))>
#<alt (/ (* tau (* x (pow (PI) 2))) (sin (* tau (* x (PI)))))>
#<alt (/ (* tau (* x (pow (PI) 2))) (sin (* tau (* x (PI)))))>
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#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
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#<alt (* x (PI))>
#<alt (* x (PI))>
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#<alt (* x (PI))>
#<alt 1>
#<alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))>
#<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))))))))))>
#<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))))))))))))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))>
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#<alt (+ 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))))))))>
#<alt (* tau (* x (PI)))>
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#<alt (* 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)))))))))>
#<alt 1>
#<alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))>
#<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))))))))))>
#<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))))))))))))))>
#<alt 1>
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#<alt (/ 1 (* x (PI)))>
#<alt (/ (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (PI)))) (/ 1 (PI))) x)>
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#<alt (* tau (* x (PI)))>
#<alt (* x (+ (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 3)))) (* tau (PI))))>
#<alt (* 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))))))))>
#<alt (* 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)))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (/ -1 (* x (PI)))>
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#<alt (/ (- (* (pow x 2) (+ (* 1/6 (* (pow tau 2) (PI))) (* (pow x 2) (+ (* -1/120 (* (pow tau 4) (pow (PI) 3))) (* 1/5040 (* (pow tau 6) (* (pow x 2) (pow (PI) 5)))))))) (/ 1 (PI))) x)>
#<alt 1>
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#<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))))))))))))))>
#<alt (* -1 (* x (PI)))>
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#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* 1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5)))) (* -1/6 (pow (PI) 3)))) (PI)))>
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#<alt 1>
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#<alt (+ 1 (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 (/ (* (+ (* -1/6 (* tau (pow (PI) 4))) (* -1/6 (* (pow tau 3) (pow (PI) 4)))) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))) (* tau (pow (PI) 2)))) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))))) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* -1/6 (* tau (pow (PI) 4))) (* -1/6 (* (pow tau 3) (pow (PI) 4)))) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))) (* tau (pow (PI) 2)))) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))) (+ (* -1/6 (* tau (pow (PI) 4))) (* -1/6 (* (pow tau 3) (pow (PI) 4))))) (* tau (pow (PI) 2)))) (+ (* -1 (/ (* (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))) (+ (* 1/120 (* tau (pow (PI) 6))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 6))) (* 1/36 (* (pow tau 3) (pow (PI) 6)))))) (* tau (pow (PI) 2)))) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))) (+ (* -1 (/ (* (+ (* -1/6 (* tau (pow (PI) 4))) (* -1/6 (* (pow tau 3) (pow (PI) 4)))) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))) (* tau (pow (PI) 2)))) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))))) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))))>
#<alt 1>
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#<alt (PI)>
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#<alt (* tau (* x (pow (PI) 2)))>
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#<alt (* x (PI))>
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#<alt tau>
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#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
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#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (/ (sin (* tau (* x (PI)))) (* x (PI)))>
#<alt (/ (sin (* tau (* x (PI)))) (* x (PI)))>
#<alt (/ (sin (* tau (* x (PI)))) (* x (PI)))>
#<alt (/ (sin (* tau (* x (PI)))) (* x (PI)))>

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	x	@	-inf	((/ 1 (/ 1 (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (/ 1 (/ 1 (* x (PI))))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* (PI) (* x tau))) (* (PI) (* x tau)) (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau)))) (* (neg (sin (* x (PI)))) (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau))))) (neg (sin (* x (PI)))) (sin (* x (PI))) (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x)) (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (* (PI) (* (PI) (* x tau))) (/ (sin (/ 1 (/ 1 (* x (PI))))) (* x (PI))) (* x (PI)) (/ (sin (* (PI) (* x tau))) (* x (PI))))
8.0ms	tau	@	-inf	((/ 1 (/ 1 (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (/ 1 (/ 1 (* x (PI))))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* (PI) (* x tau))) (* (PI) (* x tau)) (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau)))) (* (neg (sin (* x (PI)))) (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau))))) (neg (sin (* x (PI)))) (sin (* x (PI))) (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x)) (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (* (PI) (* (PI) (* x tau))) (/ (sin (/ 1 (/ 1 (* x (PI))))) (* x (PI))) (* x (PI)) (/ (sin (* (PI) (* x tau))) (* x (PI))))
6.0ms	x	@	inf	((/ 1 (/ 1 (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (/ 1 (/ 1 (* x (PI))))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* (PI) (* x tau))) (* (PI) (* x tau)) (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau)))) (* (neg (sin (* x (PI)))) (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau))))) (neg (sin (* x (PI)))) (sin (* x (PI))) (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x)) (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (* (PI) (* (PI) (* x tau))) (/ (sin (/ 1 (/ 1 (* x (PI))))) (* x (PI))) (* x (PI)) (/ (sin (* (PI) (* x tau))) (* x (PI))))
5.0ms	x	@	0	((/ 1 (/ 1 (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (/ 1 (/ 1 (* x (PI))))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* (PI) (* x tau))) (* (PI) (* x tau)) (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau)))) (* (neg (sin (* x (PI)))) (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau))))) (neg (sin (* x (PI)))) (sin (* x (PI))) (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x)) (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (* (PI) (* (PI) (* x tau))) (/ (sin (/ 1 (/ 1 (* x (PI))))) (* x (PI))) (* x (PI)) (/ (sin (* (PI) (* x tau))) (* x (PI))))
4.0ms	tau	@	inf	((/ 1 (/ 1 (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (/ 1 (/ 1 (* x (PI))))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* (PI) (* x tau))) (* (PI) (* x tau)) (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau)))) (* (neg (sin (* x (PI)))) (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau))))) (neg (sin (* x (PI)))) (sin (* x (PI))) (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x)) (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (* (PI) (* (PI) (* x tau))) (/ (sin (/ 1 (/ 1 (* x (PI))))) (* x (PI))) (* x (PI)) (/ (sin (* (PI) (* x tau))) (* x (PI))))

simplify323.0ms (2.4%)

Memory

-5.6MiB live, 568.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12 450×	`lower-fma.f64`
12 450×	`lower-fma.f32`
8 814×	`lower-*.f64`
8 814×	`lower-*.f32`
2 764×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	460	7419
1	1568	7215
2	6663	7210
0	8080	6969

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 418

Calls

Call 1

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

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

rewrite263.0ms (2%)

Memory

36.1MiB live, 468.3MiB allocated

Rules

3 616×	`lower-*.f64`
3 598×	`lower-*.f32`
2 734×	`lower-/.f64`
2 712×	`lower-/.f32`
2 176×	`lower-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	260
0	69	244
1	244	244
2	1486	228
3	7081	228
0	8428	228

Stop Event

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

Counts

20 → 1 442

Calls

Call 1

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

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

eval268.0ms (2%)

Memory: -7.7MiB live, 652.5MiB allocated
Compiler: Compiled 76 541 to 5 190 computations (93.2% saved)

prune347.0ms (2.6%)

Memory

6.9MiB live, 692.2MiB allocated

Pruning

59 alts after pruning (58 fresh and 1 done)

	Pruned	Kept	Total
New	2 874	42	2 916
Fresh	18	16	34
Picked	4	1	5
Done	0	0	0
Total	2 896	59	2 955

Accuracy

99.8%

Counts

2 955 → 59

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.9%	(/.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))
	97.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) (neg.f32 (*.f32 x (PI.f32)))))
▶	97.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (*.f32 x tau)))
	97.6%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
	97.4%	(/.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)))))
▶	97.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
	97.3%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))))
	97.0%	(/.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 tau (*.f32 (PI.f32) (neg.f32 x))))))
	97.8%	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x)))) (.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	67.1%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (/.f32 (neg.f32 (-.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))))))) (sin.f32 (*.f32 (PI.f32) (neg.f32 x)))) x)))
	82.9%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))) (PI.f32)))) x)))
	75.4%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 (.f32 tau tau) #s(literal 1/6 binary32)) (PI.f32))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)))
	61.6%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (PI.f32)) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)))
	96.8%	(/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32)))))))
	74.8%	(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x)) (fma.f32 (.f32 x x) (.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	97.8%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (sin.f32 (*.f32 x (PI.f32))))
	97.8%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))
	97.1%	(.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)))
▶	96.7%	(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (*.f32 x (PI.f32))))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (.f32 tau (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 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (.f32 x (sqrt.f32 (PI.f32)))))) (*.f32 x (PI.f32))))
	95.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal -1/3 binary32))))
	93.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( x (PI))))) (* x (PI))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 (.f32 x x) (.f32 #s(literal -1/5040 binary32) (pow.f32 (PI.f32) #s(literal 6 binary32))))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	83.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( x (PI))))) (* x (PI))) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
	68.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( x (PI))))) (* x (PI))) #s(literal 1 binary32)))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (.f32 x (.f32 (PI.f32) (PI.f32))) tau))) (sin.f32 (.f32 x (PI.f32))))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (/.f32 (neg.f32 (.f32 (.f32 (PI.f32) (.f32 x tau)) (.f32 (PI.f32) (.f32 x tau)))) (.f32 tau (.f32 (PI.f32) (neg.f32 x))))))) (sin.f32 (*.f32 x (PI.f32))))
	67.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (/.f32 (neg.f32 (-.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))))))) (sin.f32 (*.f32 (PI.f32) (neg.f32 x)))))
	82.8%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))) (PI.f32)))))
	68.7%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin ( x (PI))) (*.f32 x (PI.f32))))
	97.5%	(.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))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (.f32 (PI.f32) (neg.f32 tau))))
	97.6%	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sin.f32 (.f32 x (PI.f32))))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	97.4%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
	97.8%	(.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))))
	96.6%	(.f32 (neg.f32 (sin.f32 (.f32 (pow.f32 (pow.f32 (.f32 x (PI.f32)) #s(literal -1/2 binary32)) #s(literal -1 binary32)) (pow.f32 (pow.f32 (.f32 x (PI.f32)) #s(literal -1/2 binary32)) #s(literal -1 binary32))))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	97.4%	(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))))
	97.3%	(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (.f32 (/.f32 #s(literal -1 binary32) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))))
	75.6%	(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 #s(approx (/ (sin (* (PI) (* x tau))) (* x (PI))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) tau)) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))))
	75.9%	(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) #s(approx (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau)))) (fma.f32 (.f32 (.f32 (.f32 x (PI.f32)) #s(literal 1/6 binary32)) tau) tau (/.f32 #s(literal -1 binary32) (.f32 x (PI.f32))))))
	82.9%	(.f32 (neg.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (PI.f32))))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))))
	76.1%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau tau) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (.f32 x x))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	75.9%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
	82.3%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 tau tau) (fma.f32 (.f32 tau tau) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x x)))) (.f32 (.f32 x (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))
	81.9%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 x (PI.f32))))
	82.9%	(.f32 #s(approx (neg (sin ( x (PI)))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal 1/6 binary32)) (neg.f32 (PI.f32))))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))))
	75.5%	#s(approx (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32)))
	97.2%	#s(approx (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) tau)))))
	61.7%	#s(approx (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	75.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
▶	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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)))
✓	60.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 3 116 to 1 707 computations (45.2% saved)

simplify187.0ms (1.4%)

Memory

18.9MiB live, 287.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))))
cost-diff	0	(/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
cost-diff	0	(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (*.f32 x (PI.f32))))
cost-diff	544	(/.f32 tau (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))
cost-diff	0	(*.f32 (PI.f32) (neg.f32 x))
cost-diff	0	(sin.f32 (*.f32 (PI.f32) (neg.f32 x)))
cost-diff	0	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
cost-diff	128	(.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x)))))
cost-diff	0	(.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))))
cost-diff	0	(fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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)))
cost-diff	320	(fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)))
cost-diff	0	(.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))
cost-diff	0	(*.f32 x x)
cost-diff	0	(fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
cost-diff	0	(sin.f32 (*.f32 x (PI.f32)))
cost-diff	0	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
cost-diff	192	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (*.f32 x tau)))

Rules

7 284×	`lower-fma.f64`
7 272×	`lower-fma.f32`
4 922×	`lower-*.f64`
4 882×	`lower-*.f32`
2 260×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	600
0	105	592
1	224	582
2	704	566
3	2766	566
4	5605	564
0	8035	557

Stop Event

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

Calls

Call 1

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

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

localize235.0ms (1.8%)

Memory

-32.8MiB live, 333.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.36166000976844204	(/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
accuracy	0.36328125	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.36947250976844204	(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
accuracy	0.41634750976844204	(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (*.f32 x (PI.f32))))
accuracy	0.35384750976844204	(.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x)))))
accuracy	0.36328125	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.37728500976844204	(.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))
accuracy	0.4020500488422101	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
accuracy	0.45150375976844204	(fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	1.58496250072115	(pow.f32 (PI.f32) #s(literal 4 binary32))
accuracy	5.778138340031283	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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)))
accuracy	0.32421875	(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
accuracy	0.375	(.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	7.832392862913621	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
accuracy	0.3359375	(*.f32 x (PI.f32))
accuracy	0.36328125	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.3991012695368841	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (*.f32 x tau)))
accuracy	0.4271087890737681	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))

Samples

136.0ms

256×

valid

Compiler

Compiled 573 to 59 computations (89.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 105.0ms

ival-mult: 39.0ms (37.3% of total)

ival-sin: 35.0ms (33.5% of total)

ival-div: 10.0ms (9.6% of total)

const: 9.0ms (8.6% of total)

ival-add: 7.0ms (6.7% of total)

ival-pow: 2.0ms (1.9% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series64.0ms (0.5%)

Memory

35.7MiB live, 73.1MiB allocated

Counts

28 → 504

Calls

Call 1

Inputs
#<alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (*.f32 x tau)))>
#<alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))>
#<alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))>
#<alt (sin.f32 (*.f32 x (PI.f32)))>
#<alt #s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))>
#<alt (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))>
#<alt (*.f32 x x)>
#<alt (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))>
#<alt (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)))>
#<alt #s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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)))>
#<alt (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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))>
#<alt (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))))>
#<alt (.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x)))))>
#<alt (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))>
#<alt (sin.f32 (*.f32 (PI.f32) (neg.f32 x)))>
#<alt (*.f32 (PI.f32) (neg.f32 x))>
#<alt (/.f32 tau (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))>
#<alt (.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (*.f32 x (PI.f32))))>
#<alt (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))>
#<alt (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))))>
#<alt (.f32 (PI.f32) (.f32 x tau))>
#<alt (*.f32 x (PI.f32))>
#<alt (*.f32 (PI.f32) (PI.f32))>
#<alt (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))>
#<alt (pow.f32 (PI.f32) #s(literal 4 binary32))>
#<alt (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32))>
#<alt (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))>
#<alt (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))>

Outputs
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (+ (sin (* x (PI))) (* -1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))))))>
#<alt (* tau (+ (sin (* x (PI))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI)))))))))))>
#<alt (* tau (+ (sin (* x (PI))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (* (pow (PI) 6) (sin (* x (PI))))))) (* 1/120 (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI))))))))))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))>
#<alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))>
#<alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))>
#<alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))>
#<alt (* -1/6 (pow (PI) 2))>
#<alt (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))>
#<alt (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))>
#<alt (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))>
#<alt 1/120>
#<alt (+ 1/120 (* 1/36 (pow tau 2)))>
#<alt (+ 1/120 (* (pow tau 2) (+ 1/36 (* 1/120 (pow tau 2)))))>
#<alt (+ 1/120 (* (pow tau 2) (+ 1/36 (* 1/120 (pow tau 2)))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4))))))>
#<alt (+ 1 (+ (* (pow tau 2) (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/36 (* (pow x 2) (pow (PI) 4)))))) (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4)))))))>
#<alt (+ 1 (+ (* (pow tau 2) (+ (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4)))) (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/36 (* (pow x 2) (pow (PI) 4))))))) (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4)))))))>
#<alt (+ 1 (+ (* (pow tau 2) (+ (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4)))) (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/36 (* (pow x 2) (pow (PI) 4))))))) (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4)))))))>
#<alt (* x (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4)))))>
#<alt (+ (* x (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4))))) (* (pow tau 2) (* x (+ (* -1/6 (pow (PI) 2)) (* 1/36 (* (pow x 2) (pow (PI) 4)))))))>
#<alt (+ (* x (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4))))) (* (pow tau 2) (+ (* 1/120 (* (pow tau 2) (* (pow x 3) (pow (PI) 4)))) (* x (+ (* -1/6 (pow (PI) 2)) (* 1/36 (* (pow x 2) (pow (PI) 4))))))))>
#<alt (+ (* x (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4))))) (* (pow tau 2) (+ (* 1/120 (* (pow tau 2) (* (pow x 3) (pow (PI) 4)))) (* x (+ (* -1/6 (pow (PI) 2)) (* 1/36 (* (pow x 2) (pow (PI) 4))))))))>
#<alt (* -1 (* tau (* x (* (PI) (sin (* -1 (* x (PI))))))))>
#<alt (* tau (+ (* -1 (* x (* (PI) (sin (* -1 (* x (PI))))))) (* 1/6 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI))))))))))>
#<alt (* tau (+ (* -1 (* x (* (PI) (sin (* -1 (* x (PI))))))) (* (pow tau 2) (+ (* -1/120 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* -1 (* x (PI)))))))) (* 1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI)))))))))))>
#<alt (* tau (+ (* -1 (* x (* (PI) (sin (* -1 (* x (PI))))))) (* (pow tau 2) (+ (* 1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI))))))) (* (pow tau 2) (+ (* -1/120 (* (pow x 5) (* (pow (PI) 5) (sin (* -1 (* x (PI))))))) (* 1/5040 (* (pow tau 2) (* (pow x 7) (* (pow (PI) 7) (sin (* -1 (* x (PI))))))))))))))>
#<alt (* -1 (/ (sin (* -1 (* x (PI)))) (* x (PI))))>
#<alt (+ (* -1 (/ (sin (* -1 (* x (PI)))) (* x (PI)))) (* 1/6 (* (pow tau 2) (* x (* (PI) (sin (* -1 (* x (PI)))))))))>
#<alt (+ (* -1 (/ (sin (* -1 (* x (PI)))) (* x (PI)))) (* (pow tau 2) (+ (* -1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI)))))))) (* 1/6 (* x (* (PI) (sin (* -1 (* x (PI))))))))))>
#<alt (+ (* -1 (/ (sin (* -1 (* x (PI)))) (* x (PI)))) (* (pow tau 2) (+ (* 1/6 (* x (* (PI) (sin (* -1 (* x (PI))))))) (* (pow tau 2) (+ (* -1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI))))))) (* 1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* -1 (* x (PI)))))))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (/ 1 (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (PI)))) (/ 1 (* x (PI))))>
#<alt (+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* 1/120 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))))) (/ 1 (* x (PI))))>
#<alt (+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (pow (PI) 5)))) (* 1/120 (* (pow x 3) (pow (PI) 3))))))) (/ 1 (* x (PI))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))>
#<alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))>
#<alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt -1/6>
#<alt (- (* -1/6 (pow tau 2)) 1/6)>
#<alt (- (* -1/6 (pow tau 2)) 1/6)>
#<alt (- (* -1/6 (pow tau 2)) 1/6)>
#<alt 1>
#<alt (+ 1 (pow tau 4))>
#<alt (+ 1 (pow tau 4))>
#<alt (+ 1 (pow tau 4))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* -1/6 (* (pow tau 2) (pow (PI) 2)))>
#<alt (* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))>
#<alt (* 1/120 (pow tau 4))>
#<alt (* (pow tau 4) (+ 1/120 (* 1/36 (/ 1 (pow tau 2)))))>
#<alt (* (pow tau 4) (+ 1/120 (+ (/ 1/120 (pow tau 4)) (* 1/36 (/ 1 (pow tau 2))))))>
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#<alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))>
#<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))))))))))>
#<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))))))))))))))>
#<alt (/ 1 (* x (PI)))>
#<alt (/ (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (PI)))) (/ 1 (PI))) x)>
#<alt (/ (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (PI))) (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 3)))))) (/ 1 (PI))) x)>
#<alt (/ (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (PI))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 6) (* (pow x 2) (pow (PI) 5)))) (* 1/120 (* (pow tau 4) (pow (PI) 3))))))) (/ 1 (PI))) x)>
#<alt (* tau (* x (PI)))>
#<alt (* x (+ (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 3)))) (* tau (PI))))>
#<alt (* 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))))))))>
#<alt (* 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)))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow x 4) (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))))>
#<alt (* (pow x 4) (+ (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))) (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2))))>
#<alt (* (pow x 4) (+ (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))) (+ (/ 1 (pow x 4)) (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2)))))>
#<alt (* (pow x 4) (+ (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))) (+ (/ 1 (pow x 4)) (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2)))))>
#<alt (* (pow x 3) (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))))>
#<alt (* (pow x 3) (+ (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))) (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2))))>
#<alt (* (pow x 3) (+ (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))) (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2))))>
#<alt (* (pow x 3) (+ (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))) (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2))))>
#<alt (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI)))))>
#<alt (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI)))))>
#<alt (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI)))))>
#<alt (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI)))))>
#<alt (/ (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (sin (* -1 (* x (PI))))>
#<alt (sin (* -1 (* x (PI))))>
#<alt (sin (* -1 (* x (PI))))>
#<alt (sin (* -1 (* x (PI))))>
#<alt (* -1 (* x (PI)))>
#<alt (* -1 (* x (PI)))>
#<alt (* -1 (* x (PI)))>
#<alt (* -1 (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow x 4) (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))))>
#<alt (* (pow x 4) (+ (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))) (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2))))>
#<alt (* (pow x 4) (+ (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))) (+ (/ 1 (pow x 4)) (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2)))))>
#<alt (* (pow x 4) (+ (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))) (+ (/ 1 (pow x 4)) (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2)))))>
#<alt (* (pow x 3) (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2))))) (* -1 (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2))))) (* -1 (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (* (pow (PI) 4) (+ (* 1/120 (+ 1 (pow tau 4))) (* 1/36 (pow tau 2))))) (* -1 (/ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (pow x 2))))))>
#<alt (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI)))))>
#<alt (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI)))))>
#<alt (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI)))))>
#<alt (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI)))))>
#<alt (/ (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* -1 (* tau (* x (PI))))) (sin (* -1 (* x (PI))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (sin (* -1 (* x (PI))))>
#<alt (sin (* -1 (* x (PI))))>
#<alt (sin (* -1 (* x (PI))))>
#<alt (sin (* -1 (* x (PI))))>
#<alt (* -1 (* x (PI)))>
#<alt (* -1 (* x (PI)))>
#<alt (* -1 (* x (PI)))>
#<alt (* -1 (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* (pow x 2) (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>

Calls

6 calls:

Time	Variable		Point	Expression
22.0ms	x	@	0	((/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* x (* x (+ (* x (* x (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36))))) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))))) 1) (* x (+ (* x (* x (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36))))) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)))) (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (/ (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (* (PI) (* x (* (PI) (* x tau))))) (sin (* (PI) (neg x))) (* (PI) (neg x)) (/ tau (/ 1 (* x (PI)))) (* (/ (sin (/ tau (/ 1 (* x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (/ tau (/ 1 (* x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (sin (/ tau (/ 1 (* x (PI))))) (* (PI) (* x tau)) (* x (PI)) (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6) (pow (PI) 4) (+ (* (* tau tau) (* tau tau)) 1) (* (PI) (* x (* (PI) (* x tau)))) (* (PI) (* (PI) (* x tau))))
7.0ms	tau	@	inf	((/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* x (* x (+ (* x (* x (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36))))) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))))) 1) (* x (+ (* x (* x (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36))))) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)))) (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (/ (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (* (PI) (* x (* (PI) (* x tau))))) (sin (* (PI) (neg x))) (* (PI) (neg x)) (/ tau (/ 1 (* x (PI)))) (* (/ (sin (/ tau (/ 1 (* x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (/ tau (/ 1 (* x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (sin (/ tau (/ 1 (* x (PI))))) (* (PI) (* x tau)) (* x (PI)) (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6) (pow (PI) 4) (+ (* (* tau tau) (* tau tau)) 1) (* (PI) (* x (* (PI) (* x tau)))) (* (PI) (* (PI) (* x tau))))
7.0ms	tau	@	-inf	((/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* x (* x (+ (* x (* x (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36))))) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))))) 1) (* x (+ (* x (* x (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36))))) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)))) (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (/ (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (* (PI) (* x (* (PI) (* x tau))))) (sin (* (PI) (neg x))) (* (PI) (neg x)) (/ tau (/ 1 (* x (PI)))) (* (/ (sin (/ tau (/ 1 (* x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (/ tau (/ 1 (* x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (sin (/ tau (/ 1 (* x (PI))))) (* (PI) (* x tau)) (* x (PI)) (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6) (pow (PI) 4) (+ (* (* tau tau) (* tau tau)) 1) (* (PI) (* x (* (PI) (* x tau)))) (* (PI) (* (PI) (* x tau))))
6.0ms	x	@	-inf	((/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* x (* x (+ (* x (* x (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36))))) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))))) 1) (* x (+ (* x (* x (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36))))) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)))) (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (/ (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (* (PI) (* x (* (PI) (* x tau))))) (sin (* (PI) (neg x))) (* (PI) (neg x)) (/ tau (/ 1 (* x (PI)))) (* (/ (sin (/ tau (/ 1 (* x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (/ tau (/ 1 (* x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (sin (/ tau (/ 1 (* x (PI))))) (* (PI) (* x tau)) (* x (PI)) (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6) (pow (PI) 4) (+ (* (* tau tau) (* tau tau)) 1) (* (PI) (* x (* (PI) (* x tau)))) (* (PI) (* (PI) (* x tau))))
6.0ms	x	@	inf	((/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* x (* x (+ (* x (* x (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36))))) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))))) 1) (* x (+ (* x (* x (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* (* tau tau) 1/36))))) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)))) (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (/ (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (* (PI) (* x (* (PI) (* x tau))))) (sin (* (PI) (neg x))) (* (PI) (neg x)) (/ tau (/ 1 (* x (PI)))) (* (/ (sin (/ tau (/ 1 (* x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (/ tau (/ 1 (* x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (sin (/ tau (/ 1 (* x (PI))))) (* (PI) (* x tau)) (* x (PI)) (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6) (pow (PI) 4) (+ (* (* tau tau) (* tau tau)) 1) (* (PI) (* x (* (PI) (* x tau)))) (* (PI) (* (PI) (* x tau))))

simplify487.0ms (3.7%)

Memory

-17.9MiB live, 452.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 042×	`lower-fma.f64`
9 042×	`lower-fma.f32`
6 042×	`lower-*.f64`
6 042×	`lower-*.f32`
4 572×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	526	8915
1	1808	8611
2	3857	8482
3	5075	8386
0	8307	8004

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 504

Calls

Call 1

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

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

rewrite509.0ms (3.8%)

Memory

39.0MiB live, 500.6MiB allocated

Rules

5 572×	`lower-fma.f64`
5 560×	`lower-fma.f32`
4 622×	`lower-*.f64`
4 582×	`lower-*.f32`
3 784×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	406
0	105	401
1	383	367
2	2873	367
0	8579	361

Stop Event

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

Counts

28 → 1 082

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 (neg.f32 x) tau))))
(neg.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (neg.f32 (.f32 x (PI.f32)))) (.f32 x (*.f32 (PI.f32) tau))))
(exp.f32 (.f32 (log.f32 (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (*.f32 x (PI.f32)))) #s(literal -1 binary32)))
(pow.f32 (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (.f32 x (PI.f32))) #s(literal -1 binary32))
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eval367.0ms (2.8%)

Memory: 14.3MiB live, 373.3MiB allocated
Compiler: Compiled 63 827 to 4 383 computations (93.1% saved)

prune384.0ms (2.9%)

Memory

-2.7MiB live, 591.1MiB allocated

Pruning

70 alts after pruning (67 fresh and 3 done)

	Pruned	Kept	Total
New	2 032	32	2 064
Fresh	18	35	53
Picked	3	2	5
Done	0	1	1
Total	2 053	70	2 123

Accuracy

99.9%

Counts

2 123 → 70

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.9%	(/.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))
	69.7%	(/.f32 (-.f32 (cos.f32 (.f32 (neg.f32 x) (-.f32 (PI.f32) (.f32 (PI.f32) tau)))) (cos.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) (neg.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 tau (.f32 (.f32 (*.f32 x x) (PI.f32)) (PI.f32))) #s(literal 2 binary32)))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))))) (.f32 (PI.f32) (.f32 x tau)))
	83.1%	(/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32)))) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x tau)))
	97.4%	(/.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)))))
	97.2%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (.f32 (.f32 x (PI.f32)) x) (.f32 (PI.f32) tau)))
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x tau) x)))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 tau (.f32 (.f32 (.f32 x x) (PI.f32)) (PI.f32))))
	83.2%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (*.f32 x tau)))
	68.7%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x tau)))
	82.5%	(/.f32 (.f32 #s(approx (sin ( (PI) (neg x))) (neg.f32 (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32))))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
	68.4%	(/.f32 (.f32 #s(approx (sin ( (PI) (neg x))) (neg.f32 (.f32 x (PI.f32)))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
	97.3%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))))
	97.0%	(/.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 tau (*.f32 (PI.f32) (neg.f32 x))))))
	60.8%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) (.f32 x tau)))
▶	61.6%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) tau)) (.f32 (PI.f32) (.f32 x tau)))
	74.5%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (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) (fma.f32 tau (.f32 tau tau) tau))) (.f32 (PI.f32) tau)))) (.f32 (PI.f32) (.f32 x tau)))
	97.1%	(/.f32 #s(approx (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
	67.1%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (/.f32 (neg.f32 (-.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))))))) (sin.f32 (*.f32 (PI.f32) (neg.f32 x)))) x)))
	82.9%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))) (PI.f32)))) x)))
	75.4%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 (.f32 tau tau) #s(literal 1/6 binary32)) (PI.f32))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)))
	61.6%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (PI.f32)) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)))
	96.8%	(/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32)))))))
	74.8%	(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x)) (fma.f32 (.f32 x x) (.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
▶	97.8%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (sin.f32 (*.f32 x (PI.f32))))
	97.8%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32))))
	97.1%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (.f32 (PI.f32) tau) (PI.f32)))) x) (sin.f32 (*.f32 x (PI.f32))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))
	97.1%	(.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)))
✓	96.7%	(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (*.f32 x (PI.f32))))
	82.4%	(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) (PI.f32)))))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (.f32 tau (sqrt.f32 (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
	97.3%	(.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))))
	93.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( x (PI))))) (* x (PI))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 (.f32 x x) (.f32 #s(literal -1/5040 binary32) (pow.f32 (PI.f32) #s(literal 6 binary32))))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	83.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( x (PI))))) (* x (PI))) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
	68.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( x (PI))))) (* x (PI))) #s(literal 1 binary32)))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (.f32 x (.f32 (PI.f32) (PI.f32))) tau))) (sin.f32 (.f32 x (PI.f32))))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (/.f32 (neg.f32 (.f32 (.f32 (PI.f32) (.f32 x tau)) (.f32 (PI.f32) (.f32 x tau)))) (.f32 tau (.f32 (PI.f32) (neg.f32 x))))))) (sin.f32 (*.f32 x (PI.f32))))
	67.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (/.f32 (neg.f32 (-.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))))))) (sin.f32 (*.f32 (PI.f32) (neg.f32 x)))))
	82.8%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))) (PI.f32)))))
	68.7%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin ( x (PI))) (*.f32 x (PI.f32))))
	97.5%	(.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))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (.f32 (PI.f32) (neg.f32 tau))))
	97.4%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x tau)) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x (PI.f32))))))
	97.8%	(.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))))
	96.6%	(.f32 (neg.f32 (sin.f32 (.f32 (pow.f32 (pow.f32 (.f32 x (PI.f32)) #s(literal -1/2 binary32)) #s(literal -1 binary32)) (pow.f32 (pow.f32 (.f32 x (PI.f32)) #s(literal -1/2 binary32)) #s(literal -1 binary32))))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	82.9%	(.f32 (neg.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (PI.f32))))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))))
	82.3%	(.f32 #s(approx (/ (sin (/ tau (/ 1 ( x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 tau tau) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (.f32 x (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))
	96.9%	(.f32 #s(approx (/ (sin (/ tau (/ 1 ( x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
▶	81.9%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 x (PI.f32))))
	61.7%	#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.2%	#s(approx (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) tau)))))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 x x) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) (*.f32 x x) #s(literal 1 binary32)))
	75.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 x x) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (fma.f32 (.f32 x x) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (*.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)))))) x #s(literal 1 binary32)))
✓	75.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	75.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal 1/6 binary32))))) #s(literal 1 binary32)))
	66.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
	82.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (fma.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 x (.f32 x x)) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) #s(literal 1 binary32)))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (fma.f32 (.f32 x (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 x x) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))) x))) #s(literal 1 binary32)))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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)))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)))))) #s(literal 1 binary32)))
	75.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 tau tau) (.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))) (+.f32 #s(literal -1/6 binary32) (/.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32))))
▶	61.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	4.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))))))
✓	60.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 3 783 to 2 073 computations (45.2% saved)

simplify780.0ms (5.9%)

Memory

-222.6MiB live, 619.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 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	192	(/.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))
cost-diff	0	(/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)
cost-diff	0	#s(approx (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))
cost-diff	0	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 x (PI.f32))))
cost-diff	480	(fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau))))
cost-diff	0	(sin.f32 (*.f32 x (PI.f32)))
cost-diff	0	(.f32 (sin.f32 (.f32 x (PI.f32))) tau)
cost-diff	0	#s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) tau))
cost-diff	0	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) tau)) (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(.f32 #s(literal -1/6 binary32) (.f32 x x))
cost-diff	0	(fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
cost-diff	0	#s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #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 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (sin.f32 (*.f32 x (PI.f32))))
cost-diff	192	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32)))

Rules

44 116×	`lower-fma.f64`
44 110×	`lower-fma.f32`
6 796×	`lower-+.f64`
6 796×	`lower-+.f32`
4 844×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	601
0	104	587
1	222	573
2	659	559
3	2269	559
4	2916	559
5	3227	559
6	4077	559
7	5389	559
8	7395	559
9	7399	559
10	7399	559
11	7583	559
0	8001	555

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

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

localize243.0ms (1.8%)

Memory

25.5MiB live, 305.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.3359375	(*.f32 x (PI.f32))
accuracy	0.35384750976844204	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))
accuracy	0.36328125	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.4075775390737681	(/.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))
accuracy	0.521816259768442	(.f32 (.f32 tau tau) (*.f32 tau tau))
accuracy	0.6494713379159782	(.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	5.29573463224439	#s(approx (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))
accuracy	0.3359375	(*.f32 x (PI.f32))
accuracy	0.36328125	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.3991012695368841	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) tau)) (.f32 (PI.f32) (.f32 x tau)))
accuracy	11.943523913177895	#s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) tau))
accuracy	0.37890625	(.f32 #s(literal -1/6 binary32) (.f32 x x))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	7.832392862913621	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
accuracy	12.577860543777753	#s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
accuracy	0.3359375	(*.f32 x (PI.f32))
accuracy	0.36328125	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.3756637695368841	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.41634750976844204	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (sin.f32 (*.f32 x (PI.f32))))

Samples

163.0ms

256×

valid

Compiler

Compiled 483 to 55 computations (88.6% saved)

Precisions

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

ival-mult: 42.0ms (51% of total)

ival-div: 14.0ms (17% of total)

ival-sin: 10.0ms (12.1% of total)

const: 10.0ms (12.1% of total)

ival-add: 5.0ms (6.1% of total)

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

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

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

exact: 0.0ms (0% of total)

series66.0ms (0.5%)

Memory

-30.5MiB live, 60.6MiB allocated

Counts

24 → 480

Calls

Call 1

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

Outputs
#<alt (/ 1 (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (PI)))) (/ 1 (* x (PI))))>
#<alt (+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* 1/120 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))))) (/ 1 (* x (PI))))>
#<alt (+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (pow (PI) 5)))) (* 1/120 (* (pow x 3) (pow (PI) 3))))))) (/ 1 (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))>
#<alt (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4)))))))>
#<alt (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (pow (PI) 6)))) (* 1/120 (* (pow x 4) (pow (PI) 4))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))>
#<alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))>
#<alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))>
#<alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))>
#<alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))>
#<alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (+ (sin (* x (PI))) (* -1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))))))>
#<alt (* tau (+ (sin (* x (PI))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI)))))))))))>
#<alt (* tau (+ (sin (* x (PI))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (* (pow (PI) 6) (sin (* x (PI))))))) (* 1/120 (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI))))))))))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* -1/6 (* (pow tau 2) (PI)))>
#<alt (* (pow tau 2) (+ (* -1/6 (PI)) (* 1/120 (* (pow tau 2) (* (pow x 2) (pow (PI) 3))))))>
#<alt (* (pow tau 2) (+ (* -1/6 (PI)) (* 1/120 (* (pow tau 2) (* (pow x 2) (pow (PI) 3))))))>
#<alt (* (pow tau 2) (+ (* -1/6 (PI)) (* 1/120 (* (pow tau 2) (* (pow x 2) (pow (PI) 3))))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (/ 1 (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (PI)))) (/ 1 (* x (PI))))>
#<alt (+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* 1/120 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))))) (/ 1 (* x (PI))))>
#<alt (+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (pow (PI) 5)))) (* 1/120 (* (pow x 3) (pow (PI) 3))))))) (/ 1 (* x (PI))))>
#<alt (/ 1 (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (PI)))) (/ 1 (* x (PI))))>
#<alt (+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* 1/120 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))))) (/ 1 (* x (PI))))>
#<alt (+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* 1/120 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))))) (/ 1 (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<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))))>
#<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))))>
#<alt (/ (* tau (sin (* x (PI)))) x)>
#<alt (* tau (+ (* -1/6 (* (pow tau 2) (* x (* (pow (PI) 2) (sin (* x (PI))))))) (/ (sin (* x (PI))) x)))>
#<alt (* 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)))>
#<alt (* 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)))>
#<alt (* tau (* x (* (PI) (sin (* x (PI))))))>
#<alt (* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))) (* x (* (PI) (sin (* x (PI)))))))>
#<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)))))))))))>
#<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))))))))))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* 1/120 (pow tau 4))>
#<alt (* 1/120 (pow tau 4))>
#<alt (* 1/120 (pow tau 4))>
#<alt (* 1/120 (pow tau 4))>
#<alt (pow tau 4)>
#<alt (pow tau 4)>
#<alt (pow tau 4)>
#<alt (pow tau 4)>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 3))))>
#<alt (* (pow tau 4) (+ (* -1/6 (/ (PI) (pow tau 2))) (* 1/120 (* (pow x 2) (pow (PI) 3)))))>
#<alt (* (pow tau 4) (+ (* -1/6 (/ (PI) (pow tau 2))) (* 1/120 (* (pow x 2) (pow (PI) 3)))))>
#<alt (* (pow tau 4) (+ (* -1/6 (/ (PI) (pow tau 2))) (* 1/120 (* (pow x 2) (pow (PI) 3)))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
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#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* -1/6 (* (pow x 2) (pow (PI) 2)))>
#<alt (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (/ 1 (pow x 2))))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 3))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (* (pow tau 2) (PI)) (pow x 2))) (* 1/120 (* (pow tau 4) (pow (PI) 3)))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (* (pow tau 2) (PI)) (pow x 2))) (* 1/120 (* (pow tau 4) (pow (PI) 3)))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (* (pow tau 2) (PI)) (pow x 2))) (* 1/120 (* (pow tau 4) (pow (PI) 3)))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* 1/120 (* (pow tau 4) (* (pow x 3) (pow (PI) 3))))>
#<alt (* (pow x 3) (+ (* -1/6 (/ (* (pow tau 2) (PI)) (pow x 2))) (* 1/120 (* (pow tau 4) (pow (PI) 3)))))>
#<alt (* (pow x 3) (+ (* -1/6 (/ (* (pow tau 2) (PI)) (pow x 2))) (+ (* 1/120 (* (pow tau 4) (pow (PI) 3))) (/ 1 (* (pow x 4) (PI))))))>
#<alt (* (pow x 3) (+ (* -1/6 (/ (* (pow tau 2) (PI)) (pow x 2))) (+ (* 1/120 (* (pow tau 4) (pow (PI) 3))) (/ 1 (* (pow x 4) (PI))))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))>
#<alt (* (sin (* tau (* x (PI)))) (sin (* x (PI))))>
#<alt (* (sin (* tau (* x (PI)))) (sin (* x (PI))))>
#<alt (* (sin (* tau (* x (PI)))) (sin (* x (PI))))>
#<alt (* (sin (* tau (* x (PI)))) (sin (* x (PI))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* -1/6 (* (pow x 2) (pow (PI) 2)))>
#<alt (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (/ 1 (pow x 2))))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (sin (* x (PI))))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (sin (* x (PI)))>
#<alt (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 3))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (* (pow tau 2) (PI)) (pow x 2))) (* 1/120 (* (pow tau 4) (pow (PI) 3)))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (* (pow tau 2) (PI)) (pow x 2))) (* 1/120 (* (pow tau 4) (pow (PI) 3)))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (* (pow tau 2) (PI)) (pow x 2))) (* 1/120 (* (pow tau 4) (pow (PI) 3)))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* 1/120 (* (pow tau 4) (* (pow x 3) (pow (PI) 3))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/120 (* (pow tau 4) (pow (PI) 3))) (* 1/6 (/ (* (pow tau 2) (PI)) (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1/120 (* (pow tau 4) (pow (PI) 3))) (* 1/6 (/ (* (pow tau 2) (PI)) (pow x 2)))) (/ 1 (* (pow x 4) (PI))))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1/120 (* (pow tau 4) (pow (PI) 3))) (* 1/6 (/ (* (pow tau 2) (PI)) (pow x 2)))) (/ 1 (* (pow x 4) (PI))))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))>
#<alt (* (sin (* tau (* x (PI)))) (sin (* x (PI))))>
#<alt (* (sin (* tau (* x (PI)))) (sin (* x (PI))))>
#<alt (* (sin (* tau (* x (PI)))) (sin (* x (PI))))>
#<alt (* (sin (* tau (* x (PI)))) (sin (* x (PI))))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	x	@	-inf	((/ (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (* (/ (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (sin (* (PI) (* x tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (* -1/6 (* x x)) (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (sin (* x (PI))) tau) (sin (* x (PI))) (+ (* (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau)))) (* (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/ (+ (* (* x x) (+ (* (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau))))) (/ 1 (PI))) x) (/ (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (PI) tau)) (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* (PI) (* x tau)) (* x (PI)) (* (PI) (PI)) (* 1/120 (* (* tau tau) (* tau tau))) (* (* tau tau) (* tau tau)))
18.0ms	tau	@	0	((/ (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (* (/ (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (sin (* (PI) (* x tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (* -1/6 (* x x)) (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (sin (* x (PI))) tau) (sin (* x (PI))) (+ (* (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau)))) (* (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/ (+ (* (* x x) (+ (* (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau))))) (/ 1 (PI))) x) (/ (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (PI) tau)) (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* (PI) (* x tau)) (* x (PI)) (* (PI) (PI)) (* 1/120 (* (* tau tau) (* tau tau))) (* (* tau tau) (* tau tau)))
6.0ms	tau	@	inf	((/ (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (* (/ (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (sin (* (PI) (* x tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (* -1/6 (* x x)) (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (sin (* x (PI))) tau) (sin (* x (PI))) (+ (* (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau)))) (* (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/ (+ (* (* x x) (+ (* (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau))))) (/ 1 (PI))) x) (/ (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (PI) tau)) (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* (PI) (* x tau)) (* x (PI)) (* (PI) (PI)) (* 1/120 (* (* tau tau) (* tau tau))) (* (* tau tau) (* tau tau)))
6.0ms	tau	@	-inf	((/ (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (* (/ (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (sin (* (PI) (* x tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (* -1/6 (* x x)) (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (sin (* x (PI))) tau) (sin (* x (PI))) (+ (* (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau)))) (* (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/ (+ (* (* x x) (+ (* (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau))))) (/ 1 (PI))) x) (/ (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (PI) tau)) (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* (PI) (* x tau)) (* x (PI)) (* (PI) (PI)) (* 1/120 (* (* tau tau) (* tau tau))) (* (* tau tau) (* tau tau)))
6.0ms	x	@	inf	((/ (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (* (/ (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (sin (* (PI) (* x tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (* -1/6 (* x x)) (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (sin (* x (PI))) tau) (sin (* x (PI))) (+ (* (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau)))) (* (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (sin (* x (PI)))) (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/ (+ (* (* x x) (+ (* (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau))))) (/ 1 (PI))) x) (/ (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (PI) tau)) (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* (PI) (* x tau)) (* x (PI)) (* (PI) (PI)) (* 1/120 (* (* tau tau) (* tau tau))) (* (* tau tau) (* tau tau)))

simplify548.0ms (4.1%)

Memory

24.8MiB live, 334.0MiB allocated

Algorithm

1×	egg-herbie

Rules

12 206×	`lower-fma.f64`
12 206×	`lower-fma.f32`
6 292×	`lower-*.f64`
6 292×	`lower-*.f32`
6 014×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	484	8748
1	1632	8436
2	3316	8304
3	5694	8236
4	7100	8224
0	8323	7929

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 480

Calls

Call 1

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

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

rewrite594.0ms (4.5%)

Memory

20.8MiB live, 529.0MiB allocated

Rules

5 530×	`lower-fma.f64`
5 524×	`lower-fma.f32`
5 008×	`lower-*.f64`
4 970×	`lower-*.f32`
3 890×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	454
0	104	434
1	380	403
2	2805	403
0	8568	396

Stop Event

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

Counts

24 → 973

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)))))
(neg.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (neg.f32 (PI.f32)))))
(neg.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x))))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #s(literal -1 binary32))
(pow.f32 (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) x)) #s(literal -1 binary32))
(pow.f32 (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) (*.f32 x tau))) x)) #s(literal -1 binary32))
(pow.f32 (/.f32 (PI.f32) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau))))) #s(literal -1 binary32))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 x (neg.f32 (PI.f32)))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (.f32 x (neg.f32 (PI.f32)))))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (*.f32 (PI.f32) x))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (*.f32 x (neg.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) x)))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) (*.f32 x tau))) x)))
(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) x))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #s(literal 1 binary32))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) (*.f32 x tau))) x))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (PI.f32) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 tau (.f32 x (neg.f32 (PI.f32))))) (*.f32 x (neg.f32 (PI.f32))))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 tau (.f32 x (neg.f32 (PI.f32))))) (neg.f32 (neg.f32 (*.f32 x (neg.f32 (PI.f32))))))
(/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x))))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))
(/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)) (/.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 x tau)))) (PI.f32))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) (.f32 (PI.f32) (*.f32 x tau)))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (.f32 (.f32 (PI.f32) x) (*.f32 x tau)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(literal 1 binary32)) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x tau)) x)))
(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #s(literal 1 binary32)) (.f32 (.f32 tau (.f32 x (neg.f32 (PI.f32)))) (*.f32 (PI.f32) x)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) #s(literal 1 binary32)) (.f32 (PI.f32) (.f32 x tau)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) #s(literal 1 binary32)) (.f32 (.f32 x tau) (.f32 (PI.f32) x)))
(/.f32 (neg.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))))) (neg.f32 (neg.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)))))
(/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x)) (neg.f32 (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
(/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau))))) (neg.f32 (PI.f32)))
(/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x))) (.f32 tau (*.f32 x (neg.f32 (PI.f32)))))
(/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32))) (neg.f32 (.f32 (.f32 (PI.f32) x) (*.f32 x tau))))
(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) x)
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) #s(literal 1 binary32)) (.f32 (PI.f32) x))
(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (.f32 tau (.f32 x (neg.f32 (PI.f32)))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x))) tau)
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (*.f32 x tau))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))) x)
(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (.f32 (PI.f32) (.f32 x tau))) (PI.f32))
(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (.f32 (PI.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)))) #s(literal 1 binary32)) (PI.f32))
(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(/.f32 (neg.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(literal 1 binary32))) (neg.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x tau)) x))))
(/.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (neg.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 (neg.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #s(literal 1 binary32))) (neg.f32 (.f32 (.f32 tau (.f32 x (neg.f32 (PI.f32)))) (*.f32 (PI.f32) x))))
(/.f32 (neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) #s(literal 1 binary32))) (.f32 tau (.f32 x (neg.f32 (PI.f32)))))
(/.f32 (neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) #s(literal 1 binary32))) (neg.f32 (.f32 (.f32 x tau) (.f32 (PI.f32) x))))
(/.f32 (neg.f32 (neg.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))) (neg.f32 (neg.f32 (neg.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x))))))
(/.f32 (neg.f32 (neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x))) (neg.f32 (neg.f32 (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 (neg.f32 (neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))) (neg.f32 (neg.f32 (PI.f32))))
(/.f32 (neg.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (PI.f32))) (neg.f32 x))
(/.f32 (neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) #s(literal 1 binary32))) (.f32 x (neg.f32 (PI.f32))))
(/.f32 (neg.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (neg.f32 (.f32 tau (.f32 x (neg.f32 (PI.f32))))))
(/.f32 (neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))) (neg.f32 tau))
(/.f32 (neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (neg.f32 (*.f32 x tau)))
(/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))) (neg.f32 x))
(/.f32 (neg.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (PI.f32)))
(/.f32 (neg.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (.f32 (PI.f32) (PI.f32)))) (neg.f32 (.f32 x tau)))
(/.f32 (neg.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))) #s(literal 1 binary32))) (neg.f32 (PI.f32)))
(/.f32 (neg.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (neg.f32 (cbrt.f32 (PI.f32))))
(/.f32 (neg.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))) (sqrt.f32 (PI.f32)))) (neg.f32 (sqrt.f32 (PI.f32))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x tau)) x))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))
(.f32 #s(literal 1 binary32) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x tau)) x))))
(.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 tau (.f32 x (neg.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 x (neg.f32 (PI.f32)))))
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (neg.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x tau)) x)))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 x tau))) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (pow.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 x tau)))) #s(literal -1 binary32)))
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(.f32 (/.f32 #s(literal 1 binary32) x) (pow.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #s(literal -1 binary32)))
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(pow.f32 (/.f32 #s(literal 2 binary32) (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x))))) #s(literal -1 binary32))
(-.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) #s(literal 2 binary32)) (/.f32 (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 2 binary32)))
(-.f32 (/.f32 (cos.f32 (-.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 2 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 2 binary32) (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x))))))
(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x)))) #s(literal 2 binary32))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 2 binary32) (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x)))))))
(/.f32 (-.f32 (cos.f32 (-.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) (.f32 x tau)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #s(literal 2 binary32))
(/.f32 (neg.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x))))) #s(literal -2 binary32))
(/.f32 (-.f32 (.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) #s(literal 2 binary32)) (.f32 #s(literal 2 binary32) (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x))))) #s(literal 4 binary32))
(/.f32 (neg.f32 (neg.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x)))))) #s(literal 2 binary32))
(/.f32 (neg.f32 (-.f32 (cos.f32 (-.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) (.f32 x tau)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))))) #s(literal -2 binary32))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) x)))
(.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #s(literal 1/2 binary32))
(.f32 (PI.f32) (.f32 x tau))
(.f32 x (.f32 (PI.f32) tau))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 x tau) (PI.f32))
(.f32 (.f32 (PI.f32) x) tau)
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 x tau)))
(.f32 (.f32 (PI.f32) tau) x)
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) (*.f32 x tau)))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 x tau)))
(.f32 (.f32 (*.f32 x tau) #s(literal 1 binary32)) (PI.f32))
(.f32 (.f32 (*.f32 x tau) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) x))
(.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (.f32 x #s(literal 1 binary32)) (PI.f32))
(.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(exp.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 2 binary32)))
(exp.f32 (log.f32 (*.f32 (PI.f32) (PI.f32))))
(exp.f32 (.f32 (log.f32 (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)))
(exp.f32 (.f32 (.f32 #s(literal 2 binary32) (*.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32)))) #s(literal 3 binary32)))
(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 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 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 (sqrt.f32 (PI.f32)) #s(literal 4 binary32))
(pow.f32 (neg.f32 (PI.f32)) #s(literal 2 binary32))
(pow.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.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) (.f32 (PI.f32) (PI.f32))) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))))
(*.f32 (PI.f32) (PI.f32))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32)))
(.f32 (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
(.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) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (.f32 (PI.f32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.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)))
(.f32 tau (.f32 (.f32 tau (.f32 tau tau)) #s(literal 1/120 binary32)))
(.f32 #s(literal 1/120 binary32) (.f32 tau (.f32 tau (.f32 tau tau))))
(.f32 (.f32 tau tau) (.f32 #s(literal 1/120 binary32) (.f32 tau tau)))
(.f32 (.f32 tau (.f32 tau (.f32 tau tau))) #s(literal 1/120 binary32))
(.f32 (.f32 tau (.f32 tau tau)) (.f32 tau #s(literal 1/120 binary32)))
(.f32 (.f32 #s(literal 1/120 binary32) (.f32 tau tau)) (.f32 tau tau))
(.f32 (.f32 #s(literal 1/120 binary32) tau) (.f32 tau (.f32 tau tau)))
(.f32 (.f32 #s(literal 1/120 binary32) (.f32 tau (.f32 tau tau))) tau)
(.f32 (.f32 (.f32 #s(literal 1/120 binary32) (.f32 tau tau)) tau) tau)
(exp.f32 (.f32 (.f32 #s(literal 2 binary32) (log.f32 tau)) #s(literal 2 binary32)))
(exp.f32 (*.f32 (log.f32 tau) #s(literal 4 binary32)))
(exp.f32 (fma.f32 #s(literal 2 binary32) (log.f32 tau) (*.f32 #s(literal 2 binary32) (log.f32 tau))))
(pow.f32 tau #s(literal 4 binary32))
(pow.f32 (*.f32 tau tau) #s(literal 2 binary32))
(pow.f32 (.f32 tau (.f32 tau (*.f32 tau tau))) #s(literal 1 binary32))
(.f32 tau (.f32 tau (*.f32 tau tau)))
(.f32 (.f32 tau tau) (*.f32 tau tau))
(.f32 (.f32 tau (*.f32 tau tau)) tau)

eval386.0ms (2.9%)

Memory: -7.7MiB live, 376.2MiB allocated
Compiler: Compiled 48 575 to 3 006 computations (93.8% saved)

prune449.0ms (3.4%)

Memory

-15.9MiB live, 763.8MiB allocated

Pruning

85 alts after pruning (78 fresh and 7 done)

	Pruned	Kept	Total
New	1 727	28	1 755
Fresh	12	50	62
Picked	1	4	5
Done	0	3	3
Total	1 740	85	1 825

Accuracy

99.9%

Counts

1 825 → 85

Alt Table

Click to see full alt table

Status	Accuracy	Program
	69.8%	(/.f32 (/.f32 (/.f32 (-.f32 (cos.f32 (-.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) (.f32 x tau)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #s(literal 2 binary32)) (.f32 x (.f32 x (PI.f32)))) (*.f32 (PI.f32) tau))
✓	96.9%	(/.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))
	82.4%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32))))) (.f32 x (.f32 x (PI.f32)))) (.f32 (PI.f32) tau))
	69.7%	(/.f32 (-.f32 (cos.f32 (.f32 (neg.f32 x) (-.f32 (PI.f32) (.f32 (PI.f32) tau)))) (cos.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) (neg.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 tau (.f32 (.f32 (*.f32 x x) (PI.f32)) (PI.f32))) #s(literal 2 binary32)))
	69.9%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) #s(literal 2 binary32)))
	97.6%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) #s(literal 1 binary32)) (.f32 (.f32 x tau) (/.f32 (.f32 (PI.f32) x) (sin.f32 (*.f32 (PI.f32) x)))))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))))) (.f32 (PI.f32) (.f32 x tau)))
	83.1%	(/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32)))) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x tau)))
	97.4%	(/.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)))))
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) tau) (.f32 x (.f32 x (neg.f32 (PI.f32))))))
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x tau) x)))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 tau (.f32 (.f32 (.f32 x x) (PI.f32)) (PI.f32))))
	83.2%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (*.f32 x tau)))
	68.7%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x tau)))
	82.5%	(/.f32 (.f32 #s(approx (sin ( (PI) (neg x))) (neg.f32 (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32))))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
	68.4%	(/.f32 (.f32 #s(approx (sin ( (PI) (neg x))) (neg.f32 (.f32 x (PI.f32)))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
	97.3%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))))
	97.0%	(/.f32 (sin.f32 (.f32 (PI.f32) (neg.f32 x))) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 tau (*.f32 (PI.f32) (neg.f32 x))))))
	75.0%	(/.f32 #s(approx (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 tau (.f32 tau tau) tau))) (.f32 (PI.f32) tau))) (.f32 (PI.f32) tau))
	60.8%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) (.f32 x tau)))
	61.4%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) tau)) (.f32 (PI.f32) (*.f32 x tau)))
✓	61.6%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) tau)) (.f32 (PI.f32) (.f32 x tau)))
	74.5%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (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) (fma.f32 tau (.f32 tau tau) tau))) (.f32 (PI.f32) tau)))) (.f32 (PI.f32) (.f32 x tau)))
	74.5%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 tau (.f32 tau tau) tau))) (.f32 (PI.f32) tau)))) (.f32 (PI.f32) (.f32 x tau)))
	97.1%	(/.f32 #s(approx (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
	82.9%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))) (PI.f32)))) x)))
	61.6%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 x tau)) #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 tau (sin.f32 (.f32 (PI.f32) x))))))
	75.4%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 (.f32 tau tau) #s(literal 1/6 binary32)) (PI.f32))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)))
	61.6%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (PI.f32)) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)))
	74.8%	(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x)) (fma.f32 (.f32 x x) (.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
✓	97.8%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (sin.f32 (*.f32 x (PI.f32))))
	82.9%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) (PI.f32)))))
	97.8%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32))))
	97.1%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (.f32 (PI.f32) tau) (PI.f32)))) x) (sin.f32 (*.f32 x (PI.f32))))
	97.1%	(.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)))
✓	96.7%	(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (*.f32 x (PI.f32))))
	82.4%	(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) (PI.f32)))))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (.f32 tau (sqrt.f32 (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
	97.3%	(.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))))
	93.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( x (PI))))) (* x (PI))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 (.f32 x x) (.f32 #s(literal -1/5040 binary32) (pow.f32 (PI.f32) #s(literal 6 binary32))))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	83.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( x (PI))))) (* x (PI))) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
	68.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( x (PI))))) (* x (PI))) #s(literal 1 binary32)))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x))) (sin.f32 (.f32 (PI.f32) x)))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (.f32 x (.f32 (PI.f32) (PI.f32))) tau))) (sin.f32 (.f32 x (PI.f32))))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (/.f32 (neg.f32 (.f32 (.f32 (PI.f32) (.f32 x tau)) (.f32 (PI.f32) (.f32 x tau)))) (.f32 tau (.f32 (PI.f32) (neg.f32 x))))))) (sin.f32 (*.f32 x (PI.f32))))
	82.8%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))) (PI.f32)))))
	68.7%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin ( x (PI))) (*.f32 x (PI.f32))))
	97.5%	(.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 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x tau)) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x (PI.f32))))))
	97.0%	(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) x))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x x))) (.f32 (PI.f32) tau)))
	97.8%	(.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))))
	96.6%	(.f32 (neg.f32 (sin.f32 (.f32 (pow.f32 (pow.f32 (.f32 x (PI.f32)) #s(literal -1/2 binary32)) #s(literal -1 binary32)) (pow.f32 (pow.f32 (.f32 x (PI.f32)) #s(literal -1/2 binary32)) #s(literal -1 binary32))))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	82.9%	(.f32 (neg.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (PI.f32))))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))))
	96.9%	(.f32 #s(approx (/ (/ (sin ( (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
	82.3%	(.f32 #s(approx (/ (sin (/ tau (/ 1 ( x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 tau tau) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (.f32 x (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))
	81.8%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
	80.3%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) (PI.f32)))))
	66.8%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) #s(approx (sin (* x (PI))) (*.f32 x (PI.f32))))
	81.9%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 tau (.f32 tau #s(literal -1/6 binary32))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (.f32 tau (.f32 tau (.f32 tau tau)))))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (.f32 x (PI.f32))))
	81.9%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) #s(approx (+ ( (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau)))) (.f32 (.f32 tau tau) (fma.f32 (PI.f32) #s(literal -1/6 binary32) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 (.f32 tau tau) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (.f32 x (PI.f32))))
	82.0%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (.f32 (fma.f32 x (.f32 x (fma.f32 (PI.f32) (.f32 tau (.f32 tau #s(literal -1/6 binary32))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (.f32 tau (.f32 tau (.f32 tau tau))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))) (sin.f32 (.f32 x (PI.f32))))
	61.7%	#s(approx (/ (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.2%	#s(approx (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) tau)))))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 x x) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) (*.f32 x x) #s(literal 1 binary32)))
	75.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 x x) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (fma.f32 (.f32 x x) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (*.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)))))) x #s(literal 1 binary32)))
✓	75.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	66.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
	82.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (fma.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 x (.f32 x x)) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) #s(literal 1 binary32)))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (fma.f32 (.f32 x (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 x x) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))) x))) #s(literal 1 binary32)))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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)))
	81.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)))))) #s(literal 1 binary32)))
	61.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 x (.f32 x #s(literal -1/6 binary32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) #s(literal 1 binary32))))
	61.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 x #s(literal -1/6 binary32))) x #s(literal 1 binary32))))
	61.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (.f32 x (*.f32 x #s(literal -1/6 binary32)))) (PI.f32) #s(literal 1 binary32))))
	61.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
	75.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 tau tau) (.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))) (+.f32 #s(literal -1/6 binary32) (/.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32))))
	61.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 binary32)) #s(literal 1 binary32))))
✓	61.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	61.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))))
	4.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))))
✓	60.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 5 868 to 1 824 computations (68.9% saved)

regimes176.0ms (1.3%)

Memory

-6.8MiB live, 432.6MiB allocated

Counts

142 → 1

Calls

Call 1

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

44.0ms	(*.f32 x (PI.f32))
44.0ms	tau
40.0ms	(.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))))
40.0ms	x

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes103.0ms (0.8%)

Memory

32.7MiB live, 232.0MiB allocated

Counts

89 → 1

Calls

Call 1

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

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

Calls

4 calls:

27.0ms	(*.f32 x (PI.f32))
24.0ms	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	x

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes93.0ms (0.7%)

Memory

-36.3MiB live, 204.6MiB 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 (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (.f32 x (*.f32 x #s(literal -1/6 binary32)))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (.f32 (PI.f32) (PI.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(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) (.f32 x tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (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 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 x x) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
#s(approx (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x)) (fma.f32 (.f32 x x) (.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 x (.f32 x #s(literal -1/6 binary32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 tau tau) (.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))) (+.f32 #s(literal -1/6 binary32) (/.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32))))
(/.f32 #s(approx (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 tau (.f32 tau tau) tau))) (.f32 (PI.f32) tau))) (.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)) (.f32 (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32)) (/.f32 #s(literal 1 binary32) (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))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 tau (.f32 tau tau) tau))) (.f32 (PI.f32) tau)))) (.f32 (PI.f32) (.f32 x tau)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (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) (fma.f32 tau (.f32 tau tau) tau))) (.f32 (PI.f32) tau)))) (.f32 (PI.f32) (.f32 x tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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 (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (fma.f32 (.f32 x x) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (*.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)))))) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 x x) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)))))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (fma.f32 (.f32 x (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 x x) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))) x))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (fma.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 x (.f32 x x)) (.f32 (fma.f32 (fma.f32 tau (.f32 tau (.f32 tau tau)) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) #s(literal 1 binary32)))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) #s(approx (sin (* x (PI))) (*.f32 x (PI.f32))))
#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 (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (* (PI) (* x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (* (PI) 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)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 binary32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) (PI.f32)))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) tau)) (.f32 (PI.f32) (.f32 x tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( x (PI))))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x tau)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (PI.f32)) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 x tau)) #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 tau (sin.f32 (.f32 (PI.f32) x))))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) #s(approx (/ (/ (sin (* (PI) (* x tau))) (* x (PI))) (neg (* (PI) (* x tau)))) (fma.f32 (.f32 (.f32 (.f32 x (PI.f32)) #s(literal 1/6 binary32)) tau) tau (/.f32 #s(literal -1 binary32) (.f32 x (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin ( x (PI))) (*.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (sin ( (PI) (neg x))) (neg.f32 (.f32 x (PI.f32)))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) tau)) (.f32 (PI.f32) (*.f32 x tau)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau tau) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (.f32 x x))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (*.f32 x x)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (/ 1 (/ 1 ( 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 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (*.f32 x tau)))
(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 #s(approx (/ (sin (* (PI) (* x tau))) (* x (PI))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) tau)) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 (.f32 tau tau) #s(literal 1/6 binary32)) (PI.f32))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 (.f32 tau tau) #s(literal 1/36 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 #s(approx (sin ( (PI) (neg x))) (neg.f32 (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32))))) (sin.f32 (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) (PI.f32)))))
(/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32)))) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x tau)))
(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (PI.f32))))) (.f32 x (.f32 x (PI.f32)))) (.f32 (PI.f32) tau))
(.f32 #s(approx (neg (sin ( x (PI)))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal 1/6 binary32)) (neg.f32 (PI.f32))))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))))
(.f32 (neg.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (PI.f32))))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 tau tau) (fma.f32 (.f32 tau tau) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x x)))) (.f32 (.f32 x (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin (/ tau (/ 1 ( x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 tau tau) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (.f32 x (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) #s(approx (+ ( (* (* (PI) (* (PI) (PI))) (* x x)) (* 1/120 (* (* tau tau) (* tau tau)))) (* (PI) (* -1/6 (* tau tau)))) (.f32 (.f32 tau tau) (fma.f32 (PI.f32) #s(literal -1/6 binary32) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 (.f32 tau tau) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))) (PI.f32)))) x)))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (.f32 (fma.f32 x (.f32 x (fma.f32 (PI.f32) (.f32 tau (.f32 tau #s(literal -1/6 binary32))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (.f32 tau (.f32 tau (.f32 tau tau))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))) (sin.f32 (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 tau (.f32 tau #s(literal -1/6 binary32))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (.f32 tau (.f32 tau (.f32 tau tau)))))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 x x)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau))))
#s(approx (/ 1 (/ (/ (* (PI) (* (PI) (* x tau))) (sin (* (PI) (* x tau)))) (/ (sin (* x (PI))) x))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) tau)))))
(.f32 #s(approx (/ (sin (/ tau (/ 1 ( x (PI))))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (/ (sin ( (PI) (* x tau))) (* (PI) (* x tau))) (* x (PI))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32))))) (sin.f32 (*.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 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (.f32 x (.f32 (PI.f32) (PI.f32))) tau))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x))) (sin.f32 (.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
(/.f32 #s(approx (* (sin (* (PI) (neg x))) (sin (* tau (* (PI) (neg x))))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 tau (.f32 (.f32 (.f32 x x) (PI.f32)) (PI.f32))))
(/.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)))))

Outputs
(.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))))

Calls

4 calls:

23.0ms	(*.f32 x (PI.f32))
22.0ms	tau
22.0ms	x
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
97.5%	1	`x`
97.5%	1	`tau`
97.5%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
97.5%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes81.0ms (0.6%)

Memory

19.0MiB live, 177.7MiB allocated

Counts

71 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

20.0ms	tau
19.0ms	x
19.0ms	(*.f32 x (PI.f32))
19.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes112.0ms (0.8%)

Memory

20.2MiB live, 182.1MiB allocated

Counts

68 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

51.0ms	x
19.0ms	(*.f32 x (PI.f32))
19.0ms	tau
19.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
96.9%	1	`x`
96.9%	1	`(*.f32 x (PI.f32))`
96.9%	1	`tau`
96.9%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes86.0ms (0.6%)

Memory

-25.4MiB live, 171.6MiB allocated

Counts

67 → 1

Calls

Call 1

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

Outputs

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

21.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
20.0ms	tau
20.0ms	(*.f32 x (PI.f32))
19.0ms	x

Results

Accuracy	Segments	Branch
83.3%	1	`x`
83.3%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
83.3%	1	`(*.f32 x (PI.f32))`
83.3%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes60.0ms (0.5%)

Memory

8.9MiB live, 129.5MiB allocated

Counts

46 → 1

Calls

Call 1

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

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 #s(literal -1/6 binary32) (*.f32 x x)) #s(literal 1 binary32))))

Calls

4 calls:

16.0ms	(*.f32 x (PI.f32))
15.0ms	x
14.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
13.0ms	tau

Results

Accuracy	Segments	Branch
83.3%	1	`x`
83.3%	1	`(*.f32 x (PI.f32))`
83.3%	1	`tau`
83.3%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes56.0ms (0.4%)

Memory

5.2MiB live, 164.6MiB allocated

Counts

45 → 1

Calls

Call 1

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
82.0%	1	`x`
82.0%	1	`(*.f32 x (PI.f32))`
82.0%	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))))`
82.0%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes128.0ms (1%)

Memory

-12.3MiB live, 66.3MiB allocated

Counts

25 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

72.0ms	x
40.0ms	tau
8.0ms	(*.f32 x (PI.f32))
7.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
81.9%	1	`x`
81.9%	1	`(*.f32 x (PI.f32))`
81.9%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
81.9%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes28.0ms (0.2%)

Memory

28.7MiB live, 66.8MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

8.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
7.0ms	(*.f32 x (PI.f32))
6.0ms	tau
6.0ms	x

Results

Accuracy	Segments	Branch
75.5%	1	`x`
75.5%	1	`(*.f32 x (PI.f32))`
75.5%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
75.5%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes21.0ms (0.2%)

Memory

-39.2MiB live, 44.4MiB allocated

Counts

11 → 1

Calls

Call 1

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

7.0ms	(*.f32 x (PI.f32))
5.0ms	tau
4.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
4.0ms	x

Results

Accuracy	Segments	Branch
75.5%	1	`tau`
75.5%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
75.5%	1	`x`
75.5%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes16.0ms (0.1%)

Memory

7.4MiB live, 46.1MiB 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 (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (.f32 x (*.f32 x #s(literal -1/6 binary32)))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (.f32 (PI.f32) (PI.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(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* (PI) (* x tau)))) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) (.f32 x tau)))

Outputs

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

Calls

4 calls:

5.0ms	tau
4.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
4.0ms	(*.f32 x (PI.f32))
4.0ms	x

Results

Accuracy	Segments	Branch
66.9%	1	`tau`
66.9%	1	`x`
66.9%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
66.9%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes14.0ms (0.1%)

Memory

-2.2MiB live, 36.4MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

4.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
3.0ms	x
3.0ms	tau
3.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
61.5%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
61.5%	1	`x`
61.5%	1	`(*.f32 x (PI.f32))`
61.5%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes11.0ms (0.1%)

Memory

32.3MiB live, 32.3MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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))
2.0ms	tau
2.0ms	x

Results

Accuracy	Segments	Branch
61.5%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
61.5%	1	`x`
61.5%	1	`(*.f32 x (PI.f32))`
61.5%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes9.0ms (0.1%)

Memory

-19.5MiB live, 20.8MiB allocated

Accuracy

Total -18.4b remaining (-146.9%)

Threshold costs -18.4b (-146.9%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

4 calls:

4.0ms	tau
2.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
1.0ms	(*.f32 x (PI.f32))
1.0ms	x

Results

Accuracy	Segments	Branch
60.9%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
60.9%	1	`x`
60.9%	1	`(*.f32 x (PI.f32))`
60.9%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

simplify11.0ms (0.1%)

Memory

-10.9MiB live, 27.5MiB allocated

Algorithm

1×	egg-herbie

Rules

82×	`*-commutative_binary32`
2×	`1-exp_binary64`
2×	`+-commutative_binary32`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	123	591
1	168	591

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.7s (12.7%)

Memory

36.4MiB live, 1 261.8MiB allocated

Rules

16 966×	`lower-fma.f64`
16 966×	`lower-fma.f32`
12 450×	`lower-fma.f64`
12 450×	`lower-fma.f32`
9 042×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	1582
1	620	1562
2	2407	1538
3	4137	1538
4	4871	1538
5	5550	1538
6	5940	1538
7	5971	1538
8	5971	1538
0	8816	1486
0	460	7419
1	1568	7215
2	6663	7210
0	8080	6969
0	64	454
0	104	434
1	380	403
2	2805	403
0	8568	396
0	57	406
0	105	401
1	383	367
2	2873	367
0	8579	361
0	10	55
0	18	55
1	63	55
2	483	53
3	6485	53
0	8114	53
0	526	8915
1	1808	8611
2	3857	8482
3	5075	8386
0	8307	8004
0	39	260
0	69	244
1	244	244
2	1486	228
3	7081	228
0	8428	228

Stop Event

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

Compiler

Compiled 710 to 280 computations (60.6% saved)

preprocess90.0ms (0.7%)

Memory

4.1MiB live, 158.1MiB allocated

Remove

(abs x)

(abs tau)

Compiler

Compiled 1 790 to 656 computations (63.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze20.0ms (0.1%)

sample2.3s (17.6%)

explain142.0ms (1.1%)

preprocess92.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify55.0ms (0.4%)

localize41.0ms (0.3%)

series30.0ms (0.2%)

simplify445.0ms (3.4%)

rewrite197.0ms (1.5%)

eval95.0ms (0.7%)

prune188.0ms (1.4%)

simplify140.0ms (1.1%)

localize145.0ms (1.1%)

series54.0ms (0.4%)

simplify323.0ms (2.4%)

rewrite263.0ms (2%)

eval268.0ms (2%)

prune347.0ms (2.6%)

simplify187.0ms (1.4%)

localize235.0ms (1.8%)

series64.0ms (0.5%)

simplify487.0ms (3.7%)

rewrite509.0ms (3.8%)

eval367.0ms (2.8%)

prune384.0ms (2.9%)

simplify780.0ms (5.9%)

localize243.0ms (1.8%)

series66.0ms (0.5%)

simplify548.0ms (4.1%)

rewrite594.0ms (4.5%)

eval386.0ms (2.9%)

prune449.0ms (3.4%)

regimes176.0ms (1.3%)

regimes103.0ms (0.8%)

regimes93.0ms (0.7%)

regimes81.0ms (0.6%)

regimes112.0ms (0.8%)

regimes86.0ms (0.6%)

regimes60.0ms (0.5%)

regimes56.0ms (0.4%)

regimes128.0ms (1%)

regimes28.0ms (0.2%)

regimes21.0ms (0.2%)

regimes16.0ms (0.1%)

regimes14.0ms (0.1%)

regimes11.0ms (0.1%)

regimes9.0ms (0.1%)

simplify11.0ms (0.1%)

soundness1.7s (12.7%)

preprocess90.0ms (0.7%)

end0.0ms (0%)

Profiling