Metrics for Lanczos kernel

analyze25.0ms (0.2%)

Memory

-7.9MiB live, 62.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 37 to 21 computations (43.2% saved)

sample1.6s (10.9%)

Memory

40.4MiB live, 2 539.0MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 874.0ms

ival-sin: 231.0ms (26.4% of total)

const: 161.0ms (18.4% of total)

ival-mult: 154.0ms (17.6% of total)

ival-div: 150.0ms (17.2% of total)

ival-<=: 105.0ms (12% of total)

ival-pi: 39.0ms (4.5% of total)

ival-and: 23.0ms (2.6% of total)

exact: 8.0ms (0.9% of total)

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

Bogosity

preprocess77.0ms (0.5%)

Memory

16.0MiB live, 53.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs tau)

(abs x)

explain205.0ms (1.4%)

Memory

-1.3MiB live, 157.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
1	-	1	(0.9600090980529785 3.0675342082977295)	`(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

96.0ms

512×

valid

Compiler

Compiled 174 to 44 computations (74.7% saved)

Precisions

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

ival-pi: 37.0ms (45.3% of total)

ival-div: 22.0ms (26.9% of total)

ival-sin: 13.0ms (15.9% of total)

ival-mult: 9.0ms (11% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify34.0ms (0.2%)

Memory

-8.6MiB live, 29.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize39.0ms (0.3%)

Memory

-4.9MiB live, 37.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.9%	(*.f32 x (PI.f32))
✓	accuracy	98.8%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	accuracy	98.7%	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
✓	accuracy	98.6%	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

Samples

27.0ms

256×

valid

Compiler

Compiled 64 to 12 computations (81.3% saved)

Precisions

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

ival-sin: 6.0ms (40% of total)

ival-mult: 5.0ms (33.3% of total)

ival-div: 3.0ms (20% of total)

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

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

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

series41.0ms (0.3%)

Memory

0.2MiB live, 38.4MiB 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 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 (/ (* (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)))) (* 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 (* 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 (* 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)))) (* 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>
#<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 (/ (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)))) (* 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 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 (/ (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)))) (* 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 (* 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 (sin (* 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))))>
#<alt (sin (* tau (* x (PI))))>
#<alt (sin (* tau (* 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 (sin (* 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))))>
#<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 (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<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 (/ (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))) (* 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 (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>
#<alt (* x (PI))>

Calls

30 calls:

Time	Variable		Point	Expression
16.0ms	tau	@	-inf	(/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau))
4.0ms	tau	@	inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
3.0ms	x	@	0	(/ (sin (* x (PI))) (* x (PI)))
2.0ms	x	@	0	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
2.0ms	x	@	-inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))

simplify622.0ms (4.2%)

Memory

28.2MiB live, 582.6MiB 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	2413	1538
3	4145	1538
4	4880	1538
5	5560	1538
6	5950	1538
7	5981	1538
8	5981	1538
0	8826	1486

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

rewrite350.0ms (2.4%)

Memory

-4.7MiB live, 434.0MiB allocated

Algorithm

1×	batch-egg-rewrite

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

eval145.0ms (1%)

Memory: 6.8MiB live, 192.2MiB allocated
Compiler: Compiled 24 386 to 2 294 computations (90.6% saved)

prune391.0ms (2.6%)

Memory

-48.5MiB live, 344.7MiB allocated

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	984	29	1 013
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	985	29	1 014

Accuracy

99.8%

Counts

1 014 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.1%	(/.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 x (PI.f32))) (neg.f32 tau))
	97.2%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) tau) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32)))))
	68.0%	(/.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))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))) x)
	96.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (sqrt.f32 (PI.f32))))) (.f32 (*.f32 (PI.f32) tau) (sqrt.f32 (PI.f32))))
	97.6%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))
	97.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32)))))
	68.0%	(/.f32 (.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))) #s(literal 2 binary32))
▶	96.8%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) x)) (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
	97.5%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
▶	98.0%	(/.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)))))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	95.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32)))))) (*.f32 x (PI.f32))))
	86.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	71.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	97.6%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32)))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
▶	97.6%	(.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 (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)))))))
	97.6%	(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (/.f32 #s(literal -1 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))))
	85.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	79.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	65.0%	#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))))
	97.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
▶	64.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 402 to 760 computations (45.8% saved)

simplify348.0ms (2.3%)

Memory

27.7MiB live, 225.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

3 088×	`lower-*.f64`
3 060×	`lower-*.f32`
2 736×	`lower-/.f64`
2 720×	`lower-/.f32`
2 432×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	346
0	71	350
1	149	348
2	463	338
3	2130	338
4	4299	338
5	6403	338
6	7814	338
0	8139	338

Stop Event

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

Calls

Call 1

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

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

localize871.0ms (5.9%)

Memory

-4.6MiB live, 193.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.9%	(*.f32 x (PI.f32))
✓	accuracy	98.8%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) x)) (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
✓	accuracy	98.7%	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))
✓	accuracy	98.9%	(*.f32 x (PI.f32))
✓	accuracy	98.8%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	accuracy	98.7%	(sin.f32 (.f32 (.f32 (PI.f32) tau) x))
✓	accuracy	98.6%	(/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau))
✓	accuracy	98.9%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
✓	accuracy	98.7%	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))
✓	accuracy	98.5%	(.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))))
✓	accuracy	64.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
✓	accuracy	98.9%	(*.f32 x (PI.f32))
✓	accuracy	98.7%	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	accuracy	98.7%	(/.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)))))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))

Samples

630.0ms

256×

valid

Compiler

Compiled 346 to 36 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 614.0ms

ival-div: 432.0ms (70.4% of total)

ival-sin: 157.0ms (25.6% of total)

ival-mult: 21.0ms (3.4% of total)

ival-neg: 2.0ms (0.3% of total)

ival-pi: 1.0ms (0.2% of total)

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

exact: 0.0ms (0% of total)

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

series159.0ms (1.1%)

Memory

-12.4MiB live, 26.1MiB allocated

Counts

17 → 372

Calls

Call 1

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

Outputs
#<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 (/ (* (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)))) (* 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 (* 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 (* 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)))) (* 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 (* tau (* x (PI)))>
#<alt (* x (+ (* 1/6 (* tau (* (pow x 2) (pow (PI) 3)))) (* tau (PI))))>
#<alt (* x (+ (* tau (PI)) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/36 (* tau (pow (PI) 5))) (* 1/120 (* tau (pow (PI) 5)))))) (* -1/6 (* tau (pow (PI) 3)))))))>
#<alt (* x (+ (* tau (PI)) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/5040 (* tau (pow (PI) 7))) (+ (* 1/720 (* tau (pow (PI) 7))) (* 1/6 (* (pow (PI) 2) (+ (* -1/36 (* tau (pow (PI) 5))) (* 1/120 (* tau (pow (PI) 5)))))))))) (+ (* -1/36 (* tau (pow (PI) 5))) (* 1/120 (* tau (pow (PI) 5)))))) (* -1/6 (* tau (pow (PI) 3)))))))>
#<alt (/ (* tau (* (pow x 2) (pow (PI) 2))) (sin (* x (PI))))>
#<alt (/ (* tau (* (pow x 2) (pow (PI) 2))) (sin (* x (PI))))>
#<alt (/ (* tau (* (pow x 2) (pow (PI) 2))) (sin (* x (PI))))>
#<alt (/ (* tau (* (pow x 2) (pow (PI) 2))) (sin (* x (PI))))>
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#<alt (+ (* 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)))))))))))))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* tau (* (PI) (sin (* x (PI))))) x)>
#<alt (* tau (+ (* -1/6 (* (pow tau 2) (* x (* (pow (PI) 3) (sin (* x (PI))))))) (/ (* (PI) (sin (* x (PI)))) x)))>
#<alt (* tau (+ (* (pow tau 2) (+ (* -1/6 (* x (* (pow (PI) 3) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 5) (sin (* x (PI))))))))) (/ (* (PI) (sin (* x (PI)))) x)))>
#<alt (* tau (+ (* (pow tau 2) (+ (* -1/6 (* x (* (pow (PI) 3) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 7) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 5) (sin (* x (PI)))))))))) (/ (* (PI) (sin (* x (PI)))) x)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (pow x 2))>
#<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 (/ (* (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)))) (* 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 (* 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 (* 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)))) (* 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 (* tau (* x (pow (PI) 2)))>
#<alt (* x (+ (* tau (pow (PI) 2)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 4))) (* -1/6 (* (pow tau 3) (pow (PI) 4)))))))>
#<alt (* x (+ (* tau (pow (PI) 2)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 4))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 4))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 6))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 6))) (* 1/36 (* (pow tau 3) (pow (PI) 6)))))))))))>
#<alt (* x (+ (* tau (pow (PI) 2)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 4))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 4))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 6))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 6))) (+ (* 1/36 (* (pow tau 3) (pow (PI) 6))) (* (pow x 2) (+ (* -1/720 (* (pow tau 3) (pow (PI) 8))) (+ (* -1/720 (* (pow tau 5) (pow (PI) 8))) (+ (* -1/5040 (* tau (pow (PI) 8))) (* -1/5040 (* (pow tau 7) (pow (PI) 8))))))))))))))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (* tau (* (PI) (sin (* x (PI)))))>
#<alt (* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 3) (sin (* x (PI))))))) (* (PI) (sin (* x (PI))))))>
#<alt (* tau (+ (* (PI) (sin (* x (PI)))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 3) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 4) (* (pow (PI) 5) (sin (* x (PI)))))))))))>
#<alt (* tau (+ (* (PI) (sin (* x (PI)))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 3) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (* (pow (PI) 7) (sin (* x (PI))))))) (* 1/120 (* (pow x 4) (* (pow (PI) 5) (sin (* x (PI))))))))))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)>
#<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 (/ (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))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>

Calls

93 calls:

Time	Variable		Point	Expression
140.0ms	x	@	inf	(* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x))
1.0ms	tau	@	0	(* (/ (neg (* x (PI))) (sin (* x (PI)))) (neg (* (PI) (* x tau))))
1.0ms	x	@	-inf	(* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x))
1.0ms	x	@	0	(* (/ (neg (* x (PI))) (sin (* x (PI)))) (neg (* (PI) (* x tau))))
1.0ms	x	@	-inf	(* (/ (neg (* x (PI))) (sin (* x (PI)))) (neg (* (PI) (* x tau))))

simplify474.0ms (3.2%)

Memory

6.0MiB live, 843.1MiB allocated

Algorithm

1×	egg-herbie

Rules

16 822×	`lower-fma.f64`
16 822×	`lower-fma.f32`
7 888×	`lower-*.f64`
7 888×	`lower-*.f32`
5 608×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	375	6502
1	1253	6337
2	4877	6148
0	8228	5948

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

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

rewrite312.0ms (2.1%)

Memory

3.4MiB live, 796.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 574×	`lower-*.f64`
4 546×	`lower-*.f32`
4 000×	`lower-/.f64`
3 984×	`lower-/.f32`
1 274×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	220
0	71	222
1	240	212
2	1420	198
3	7834	198
0	8005	198

Stop Event

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

Counts

17 → 1 679

Calls

Call 1

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

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

eval328.0ms (2.2%)

Memory: 50.2MiB live, 911.4MiB allocated
Compiler: Compiled 77 385 to 4 967 computations (93.6% saved)

prune337.0ms (2.3%)

Memory

-22.0MiB live, 941.4MiB allocated

Pruning

45 alts after pruning (44 fresh and 1 done)

	Pruned	Kept	Total
New	3 035	36	3 071
Fresh	16	8	24
Picked	4	1	5
Done	0	0	0
Total	3 055	45	3 100

Accuracy

99.8%

Counts

3 100 → 45

Alt Table

Click to see full alt table

Status	Accuracy	Program
	67.8%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 x x) #s(literal 2 binary32))) (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
	97.0%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 (PI.f32) x) (*.f32 (PI.f32) x))) tau)
	67.9%	(/.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 x (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
	68.0%	(/.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))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))) x)
	97.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32)))))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 x tau))
	85.1%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) x)) (/.f32 #s(literal 1 binary32) x)) (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
	97.2%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 x x)))) (*.f32 (PI.f32) (PI.f32)))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 tau (.f32 (PI.f32) (PI.f32))) (.f32 x x)))
▶	97.7%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
	64.1%	(/.f32 (.f32 #s(approx ( (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (.f32 x (.f32 tau (.f32 (PI.f32) (PI.f32))))) (/.f32 #s(literal 1 binary32) x)) (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
	85.1%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (* (/ (neg (* x (PI))) (sin (* x (PI)))) (neg (* (PI) (* x tau)))) (.f32 x (.f32 tau (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal 1/6 binary32) (PI.f32))))))
	71.0%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (* (/ (neg (* x (PI))) (sin (* x (PI)))) (neg (* (PI) (* x tau)))) (.f32 x (.f32 tau (PI.f32)))))
▶	64.0%	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) tau)))
	97.2%	(.f32 (/.f32 (sin.f32 (/.f32 (-.f32 #s(literal 0 binary32) (pow.f32 (.f32 (PI.f32) (neg.f32 x)) #s(literal 3 binary32))) (+.f32 #s(literal 0 binary32) (fma.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) x) (.f32 #s(literal 0 binary32) (.f32 (PI.f32) (neg.f32 x))))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	85.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) (exp.f32 (.f32 (log.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1 binary32))))
▶	85.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	71.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	95.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32)))))) (*.f32 x (PI.f32))))
	86.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	71.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) x)))
	97.5%	(.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))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (PI.f32) x) (*.f32 (PI.f32) x))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) x) tau)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
▶	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (/.f32 (*.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (.f32 (PI.f32) tau) x)))
	85.6%	(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	71.1%	(.f32 (/.f32 #s(approx (sin ( x (PI))) (.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 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.6%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.6%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	96.1%	(.f32 (exp.f32 (.f32 (log.f32 (/.f32 (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1 binary32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	90.8%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) tau) (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	85.4%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	71.1%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	85.7%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (* (PI) (* (PI) tau))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	79.7%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (* (PI) (* (PI) tau))) (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)))
	97.2%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (* (PI) (* (PI) tau))) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))
	65.0%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (* (PI) (* (PI) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
✓	64.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 2 230 to 1 249 computations (44% saved)

simplify125.0ms (0.8%)

Memory

2.0MiB live, 120.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

2 520×	`lower-*.f64`
2 480×	`lower-*.f32`
1 966×	`associate-*l/`
1 102×	`associate-/r*`
820×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	425
0	86	425
1	171	421
2	392	421
3	1232	421
4	2724	421
5	2965	421
6	2965	421
7	4045	421
8	4170	421
9	4170	421
10	4288	421
11	4288	421
0	4288	421

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize156.0ms (1.1%)

Memory

-14.7MiB live, 313.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.9%	(*.f32 x (PI.f32))
✓	accuracy	98.8%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32))))
✓	accuracy	98.7%	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))
✓	accuracy	98.9%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (*.f32 (PI.f32) tau) x))))
✓	accuracy	98.7%	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))
✓	accuracy	98.5%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
✓	accuracy	98.7%	(sin.f32 (.f32 (.f32 (PI.f32) tau) x))
✓	accuracy	98.6%	(/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	86.8%	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32)))
✓	accuracy	98.8%	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) tau)))
✓	accuracy	98.8%	(.f32 tau (.f32 (PI.f32) (PI.f32)))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	65.2%	#s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (.f32 tau (.f32 (PI.f32) (PI.f32))))
✓	accuracy	98.9%	(*.f32 (PI.f32) x)
✓	accuracy	98.8%	(.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))
✓	accuracy	98.7%	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))

Samples

91.0ms

256×

valid

Compiler

Compiled 394 to 45 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-mult: 36.0ms (50.1% of total)

ival-div: 16.0ms (22.3% of total)

ival-sin: 12.0ms (16.7% of total)

const: 4.0ms (5.6% of total)

ival-pi: 2.0ms (2.8% of total)

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

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

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

exact: 0.0ms (0% of total)

series29.0ms (0.2%)

Memory

1.5MiB live, 39.1MiB allocated

Counts

23 → 456

Calls

Call 1

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

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

Calls

114 calls:

Time	Variable		Point	Expression
10.0ms	tau	@	-inf	(/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau))))
1.0ms	tau	@	0	(/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau))))
1.0ms	tau	@	-inf	(* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI))))
1.0ms	x	@	-inf	(/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau))))
1.0ms	tau	@	inf	(* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI))))

simplify543.0ms (3.7%)

Memory

-4.4MiB live, 600.9MiB allocated

Algorithm

1×	egg-herbie

Rules

17 258×	`lower-fma.f64`
17 258×	`lower-fma.f32`
7 828×	`lower-*.f64`
7 828×	`lower-*.f32`
5 578×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	397	7508
1	1323	7326
2	5149	7116
0	8144	6882

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 455

Calls

Call 1

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

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

rewrite426.0ms (2.9%)

Memory

20.9MiB live, 368.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 374×	`lower-*.f64`
5 334×	`lower-*.f32`
4 800×	`lower-/.f64`
4 788×	`lower-/.f32`
3 092×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	289
0	86	285
1	274	285
2	1495	273
0	8431	271

Stop Event

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

Counts

23 → 1 532

Calls

Call 1

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

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

eval385.0ms (2.6%)

Memory: 14.1MiB live, 314.3MiB allocated
Compiler: Compiled 58 552 to 3 760 computations (93.6% saved)

prune600.0ms (4%)

Memory

4.3MiB live, 650.7MiB allocated

Pruning

93 alts after pruning (90 fresh and 3 done)

	Pruned	Kept	Total
New	2 378	68	2 446
Fresh	17	22	39
Picked	3	2	5
Done	0	1	1
Total	2 398	93	2 491

Accuracy

99.8%

Counts

2 491 → 93

Alt Table

Click to see full alt table

Status	Accuracy	Program
	67.9%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) #s(literal 1/2 binary32)) (.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) #s(literal 1/2 binary32))) (.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)))) (fma.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) #s(literal 1/2 binary32) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
	67.8%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 x x) #s(literal 2 binary32))) (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
	68.0%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 tau (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))) x)
	67.9%	(/.f32 (/.f32 (.f32 (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) #s(literal 3 binary32)) (pow.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 3 binary32))) #s(literal 1/2 binary32)) (+.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (-.f32 x (.f32 x tau))))))) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (+.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
	85.5%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (PI.f32) x)) tau)
	85.5%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) x) (.f32 (PI.f32) tau))
	97.0%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 (PI.f32) x) (*.f32 (PI.f32) x))) tau)
	64.1%	(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (.f32 (PI.f32) (.f32 (PI.f32) tau))) (PI.f32)) (*.f32 (PI.f32) tau))
	97.3%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))))) x)
	67.9%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32))))) #s(literal 2 binary32)))
	68.0%	(/.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)))
	85.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (neg.f32 x))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (neg.f32 tau))
	85.5%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) x)
	85.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) tau)) x)
	85.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 x tau))
	97.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32)))))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 x tau))
	64.1%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (.f32 (PI.f32) (.f32 (PI.f32) tau)))) tau)
	85.5%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) (.f32 (PI.f32) tau))) x)
	85.7%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) (.f32 x tau))) (PI.f32))
	85.8%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) (PI.f32))) (.f32 x tau))
	85.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) x)) (.f32 (PI.f32) tau))
▶	86.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (PI.f32) (*.f32 x tau)))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (.f32 (PI.f32) tau) x))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
	97.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x tau))) (PI.f32)))
▶	98.0%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 (PI.f32) (.f32 x tau)) (.f32 (PI.f32) x)))
	85.6%	(/.f32 (.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.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)))) (sin.f32 (*.f32 x (PI.f32)))) x)
	85.6%	(/.f32 (.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* (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 (.f32 x x) (.f32 x x)))) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))) (sin.f32 (*.f32 x (PI.f32)))) x)
	85.7%	(/.f32 (.f32 #s(approx (sin ( (PI) x)) (.f32 x (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
	71.1%	(/.f32 (.f32 #s(approx (sin ( (PI) x)) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
	85.1%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (* (/ (neg (* x (PI))) (sin (* x (PI)))) (neg (* (PI) (* x tau)))) (.f32 x (.f32 tau (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal 1/6 binary32) (PI.f32))))))
	71.0%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (* (/ (neg (* x (PI))) (sin (* x (PI)))) (neg (* (PI) (* x tau)))) (.f32 x (.f32 tau (PI.f32)))))
	85.9%	(/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	85.2%	(/.f32 #s(approx (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) (fma.f32 x (.f32 (.f32 x x) (fma.f32 (.f32 x 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))))) x)) x)
	64.9%	(/.f32 #s(approx (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))) x)
	79.4%	(/.f32 #s(approx (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) x)
	85.3%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) x) (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) tau)))
	85.7%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x tau) (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (PI.f32))))
	85.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) tau)) x) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.8%	(.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (PI.f32)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.5%	(.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) tau) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.4%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (PI.f32) tau)) (/.f32 #s(literal 1 binary32) x))
	85.8%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
	97.2%	(.f32 (/.f32 (sin.f32 (/.f32 (-.f32 #s(literal 0 binary32) (pow.f32 (.f32 (PI.f32) (neg.f32 x)) #s(literal 3 binary32))) (+.f32 #s(literal 0 binary32) (fma.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) x) (.f32 #s(literal 0 binary32) (.f32 (PI.f32) (neg.f32 x))))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	85.4%	(.f32 (/.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	86.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
✓	85.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	71.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	95.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32)))))) (*.f32 x (PI.f32))))
	71.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	85.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) tau))
▶	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32)))))) (sin.f32 (.f32 (PI.f32) x)))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (PI.f32) x) (*.f32 (PI.f32) x))))
	85.4%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) (.f32 (PI.f32) x)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) x) tau)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (/.f32 (*.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (.f32 (.f32 (PI.f32) tau) x)))
✓	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (.f32 (PI.f32) tau) x)))
	86.0%	(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	79.5%	(.f32 (/.f32 #s(approx (sin ( (* (PI) tau) x)) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	79.9%	(.f32 (/.f32 #s(approx (sin ( (* (PI) tau) x)) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x x)))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.6%	(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	85.3%	(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	71.0%	(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	85.9%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32)))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 (PI.f32) x))))
	67.9%	(.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (.f32 tau (.f32 x (*.f32 (PI.f32) (PI.f32))))) #s(literal 2 binary32))))
	85.7%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.4%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	97.4%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.6%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.6%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	86.0%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	84.8%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 tau tau) (.f32 tau tau)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	80.4%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	84.8%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau tau) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau tau) (.f32 (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 (.f32 x x) (.f32 x x))))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	86.2%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
▶	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
▶	85.4%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	71.1%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	90.8%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) tau) (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	79.7%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) x) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
	85.7%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x 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)))
	65.0%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) x) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	79.7%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (* (PI) (* (PI) tau))) (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)))
✓	64.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 5 143 to 2 835 computations (44.9% saved)

simplify48.0ms (0.3%)

Memory

-15.5MiB live, 64.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Program
✓	cost-diff	(.f32 (PI.f32) (.f32 x tau))
✓	cost-diff	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	cost-diff	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32))))))
✓	cost-diff	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32)))))) (sin.f32 (.f32 (PI.f32) x)))
✓	cost-diff	(fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (*.f32 tau (PI.f32))))
✓	cost-diff	(/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (*.f32 tau (PI.f32)))) x)
✓	cost-diff	#s(approx (/ (sin (* x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (*.f32 tau (PI.f32)))) x))
✓	cost-diff	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
✓	cost-diff	(.f32 (PI.f32) (.f32 x tau))
✓	cost-diff	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	cost-diff	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))))
✓	cost-diff	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (PI.f32) (*.f32 x tau)))
✓	cost-diff	(fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
✓	cost-diff	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32)))
✓	cost-diff	#s(approx (/ (sin (* (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32))
✓	cost-diff	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
✓	cost-diff	(*.f32 (PI.f32) x)
✓	cost-diff	(sin.f32 (*.f32 (PI.f32) x))
✓	cost-diff	(.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
✓	cost-diff	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 (PI.f32) (.f32 x tau)) (.f32 (PI.f32) x)))

Rules

926×	`lower-*.f64`
888×	`lower-*.f32`
684×	`associate-/r*`
650×	`lower-/.f64`
646×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	508
0	89	508
1	185	508
2	426	508
3	1041	508
4	1532	508
5	1583	508
6	1587	508
0	1587	508

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize238.0ms (1.6%)

Memory

17.6MiB live, 331.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.7%	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))
✓	accuracy	98.6%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32)))))) (sin.f32 (.f32 (PI.f32) x)))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	98.7%	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))
✓	accuracy	98.5%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
✓	accuracy	87.1%	#s(approx (/ (sin (* x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (*.f32 tau (PI.f32)))) x))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))
✓	accuracy	98.5%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (PI.f32) (*.f32 x tau)))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	86.8%	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
✓	accuracy	99.3%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	86.8%	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32)))
✓	accuracy	65.0%	#s(approx (/ (sin (* (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32))
✓	accuracy	98.9%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
✓	accuracy	98.9%	(*.f32 (PI.f32) x)
✓	accuracy	98.7%	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))

Samples

159.0ms

256×

valid

Compiler

Compiled 421 to 52 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 139.0ms

ival-mult: 100.0ms (72% of total)

ival-div: 17.0ms (12.2% of total)

ival-sin: 12.0ms (8.6% of total)

const: 4.0ms (2.9% of total)

ival-add: 3.0ms (2.2% of total)

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

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.2%)

Memory

6.3MiB live, 44.3MiB allocated

Counts

20 → 396

Calls

Call 1

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

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

Calls

99 calls:

Time	Variable		Point	Expression
4.0ms	tau	@	inf	(/ (+ (* x (* x (/ (* -1/6 (PI)) tau))) (/ 1 (* tau (PI)))) x)
1.0ms	tau	@	0	(/ (+ (* x (* x (/ (* -1/6 (PI)) tau))) (/ 1 (* tau (PI)))) x)
1.0ms	tau	@	-inf	(/ (sin (* (PI) (* x tau))) (* x (* tau (* x (* (PI) (PI))))))
1.0ms	tau	@	-inf	(/ (+ (* x (* x (/ (* -1/6 (PI)) tau))) (/ 1 (* tau (PI)))) x)
1.0ms	x	@	0	(/ (+ (* x (* x (/ (* -1/6 (PI)) tau))) (/ 1 (* tau (PI)))) x)

simplify612.0ms (4.1%)

Memory

-19.6MiB live, 1 105.4MiB allocated

Algorithm

1×	egg-herbie

Rules

24 526×	`lower-fma.f64`
24 526×	`lower-fma.f32`
7 346×	`lower-*.f64`
7 346×	`lower-*.f32`
6 116×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	440	7051
1	1456	6895
2	5517	6691
0	8386	6440

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 396

Calls

Call 1

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

rewrite364.0ms (2.5%)

Memory

29.0MiB live, 815.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 070×	`lower-fma.f64`
7 066×	`lower-fma.f32`
4 508×	`lower-*.f64`
4 470×	`lower-*.f32`
4 270×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	343
0	89	343
1	323	343
2	1752	327
0	8447	321

Stop Event

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

Counts

20 → 736

Calls

Call 1

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

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

eval188.0ms (1.3%)

Memory: 2.0MiB live, 313.9MiB allocated
Compiler: Compiled 42 981 to 2 873 computations (93.3% saved)

prune541.0ms (3.6%)

Memory

-251.4MiB live, 673.1MiB allocated

Pruning

120 alts after pruning (117 fresh and 3 done)

	Pruned	Kept	Total
New	1 509	58	1 567
Fresh	26	59	85
Picked	4	1	5
Done	1	2	3
Total	1 540	120	1 660

Accuracy

99.9%

Counts

1 660 → 120

Alt Table

Click to see full alt table

Status	Accuracy	Program
	67.9%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) #s(literal 1/2 binary32)) (.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) #s(literal 1/2 binary32))) (.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)))) (fma.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) #s(literal 1/2 binary32) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
	67.8%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 (.f32 x tau) x))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 x x) #s(literal 2 binary32))) (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
	68.0%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 tau (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))) x)
	67.9%	(/.f32 (/.f32 (.f32 (-.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) #s(literal 3 binary32)) (pow.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 3 binary32))) #s(literal 1/2 binary32)) (+.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (-.f32 x (.f32 x tau))))))) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (+.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))))))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
	85.5%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))) (.f32 (PI.f32) x)) tau)
	85.5%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))) x) (.f32 (PI.f32) tau))
	97.0%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 (PI.f32) x) (*.f32 (PI.f32) x))) tau)
	97.9%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) x)) (.f32 (PI.f32) (*.f32 x tau)))
	64.1%	(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (.f32 (PI.f32) (.f32 (PI.f32) tau))) (PI.f32)) (*.f32 (PI.f32) tau))
	97.3%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))))) x)
	67.9%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32))))) #s(literal 2 binary32)))
	67.9%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) (cos.f32 (.f32 (PI.f32) (+.f32 x (.f32 x tau))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))) #s(literal 2 binary32)))
	68.0%	(/.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)))
	85.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) tau)) x)
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 x tau))
	64.1%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (.f32 (PI.f32) (.f32 (PI.f32) tau)))) tau)
	85.4%	(/.f32 (.f32 (sin.f32 (/.f32 x (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (PI.f32) (*.f32 x tau)))
	85.5%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (PI.f32) (*.f32 x tau)))
	85.5%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (PI.f32) (*.f32 x tau)))
	85.7%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32))) (.f32 x tau))) (PI.f32))
	85.5%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) (.f32 (PI.f32) tau))) x)
	85.8%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))) (PI.f32))) (.f32 x tau))
	85.4%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (*.f32 (PI.f32) x) tau))
	85.5%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (*.f32 (PI.f32) tau) x))
	71.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 x tau)))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (.f32 (PI.f32) tau) x))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau)))))
	97.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 (.f32 (PI.f32) x) tau) (.f32 (PI.f32) x)))
	97.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x tau))) (PI.f32)))
	85.6%	(/.f32 (.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.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)))) (sin.f32 (*.f32 x (PI.f32)))) x)
	85.6%	(/.f32 (.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* (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 (.f32 x x) (.f32 x x)))) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))) (sin.f32 (*.f32 x (PI.f32)))) x)
	79.4%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (PI.f32) (*.f32 x tau)))
	79.5%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 x (.f32 x x))))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (.f32 (PI.f32) (*.f32 x tau)))
	85.9%	(/.f32 (.f32 #s(approx (sin ( (PI) x)) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 (PI.f32) (.f32 x tau)) (*.f32 (PI.f32) x)))
	85.7%	(/.f32 (.f32 #s(approx (sin ( (PI) x)) (.f32 x (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
	71.1%	(/.f32 (.f32 #s(approx (sin ( (PI) x)) (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (*.f32 x tau)))))
	85.1%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (* (/ (neg (* x (PI))) (sin (* x (PI)))) (neg (* (PI) (* x tau)))) (.f32 x (.f32 tau (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal 1/6 binary32) (PI.f32))))))
	71.0%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (* (/ (neg (* x (PI))) (sin (* x (PI)))) (neg (* (PI) (* x tau)))) (.f32 x (.f32 tau (PI.f32)))))
	85.9%	(/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32))) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	85.2%	(/.f32 #s(approx (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) (fma.f32 x (.f32 (.f32 x x) (fma.f32 (.f32 x 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))))) x)) x)
	64.9%	(/.f32 #s(approx (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))) x)
	79.4%	(/.f32 #s(approx (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) x)
	78.5%	(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) (.f32 tau (PI.f32))))) (.f32 (PI.f32) (.f32 x tau)))
	64.0%	(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (PI.f32) (.f32 x tau)))
	85.3%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) x) (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))) tau)))
	85.4%	(/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 (PI.f32) (*.f32 x tau))) (PI.f32))) tau)))
	85.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) tau)) x) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.8%	(.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (PI.f32)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.5%	(.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) tau) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.4%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))) (.f32 (PI.f32) tau)) (/.f32 #s(literal 1 binary32) x))
	85.8%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
	85.4%	(.f32 (/.f32 (.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 (PI.f32) (*.f32 x tau))) (PI.f32))) x) (/.f32 #s(literal 1 binary32) tau))
	97.2%	(.f32 (/.f32 (sin.f32 (/.f32 (-.f32 #s(literal 0 binary32) (pow.f32 (.f32 (PI.f32) (neg.f32 x)) #s(literal 3 binary32))) (+.f32 #s(literal 0 binary32) (fma.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) x) (.f32 #s(literal 0 binary32) (.f32 (PI.f32) (neg.f32 x))))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	85.4%	(.f32 (/.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	86.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	71.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32)))))) (sin.f32 (.f32 (PI.f32) x)))
	95.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32)))))) (*.f32 x (PI.f32))))
	71.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	85.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32))) tau))
	85.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) tau)) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32))) x))
	94.4%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 x (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 6 binary32)))))) (sin.f32 (*.f32 (PI.f32) x)))
✓	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32)))))) (sin.f32 (.f32 (PI.f32) x)))
	85.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32)))))) #s(approx (sin ( (PI) x)) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (PI.f32) x) (*.f32 (PI.f32) x))))
	85.4%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32))) (.f32 (PI.f32) x)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) x) tau)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (/.f32 (*.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))))
✓	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	86.0%	(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	79.5%	(.f32 (/.f32 #s(approx (sin ( (* (PI) tau) x)) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	79.9%	(.f32 (/.f32 #s(approx (sin ( (* (PI) tau) x)) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x x)))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	85.6%	(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	71.0%	(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	85.9%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (.f32 x (.f32 (PI.f32) (PI.f32)))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 (PI.f32) x))))
	85.7%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x tau)) (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 (PI.f32) (*.f32 x tau))) (PI.f32))))
	67.9%	(.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (-.f32 x (.f32 x tau)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (.f32 tau (.f32 x (*.f32 (PI.f32) (PI.f32))))) #s(literal 2 binary32))))
	85.4%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	97.4%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.6%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.6%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	80.4%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	84.8%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	80.4%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32))))))
	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) x) (*.f32 (PI.f32) x)) #s(literal -1/6 binary32) #s(literal 1 binary32))))
	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) x))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 x (.f32 x #s(literal -1/6 binary32))) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 binary32)))) #s(literal 1 binary32))))
	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (*.f32 x x) (PI.f32))) #s(literal 1 binary32))))
	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 (fma.f32 (.f32 #s(literal 1/36 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 x x) (.f32 x x)) #s(literal -1 binary32)) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32))) (.f32 x x) #s(literal -1 binary32)))))
	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) x)) (.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) x))) #s(literal 1/36 binary32))) (-.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) #s(literal -1/6 binary32)))))))))
	65.1%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) x)) (.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) x))) #s(literal 1/36 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) #s(literal -1/6 binary32))))))))))
	4.2%	(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))))))
	85.8%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* tau (* x (* (PI) (PI)))))) (fma.f32 (.f32 tau tau) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 x (.f32 x x)))) (.f32 (.f32 tau tau) #s(literal 1/120 binary32)) (.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (.f32 (PI.f32) x)))
	80.0%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* tau (* x (* (PI) (PI)))))) (fma.f32 tau (.f32 tau (.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 (PI.f32) x)))
	85.4%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* tau (* x (* (PI) (PI)))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 tau tau) (.f32 tau tau)) (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 (PI.f32) x)))
	64.9%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* tau (* x (* (PI) (PI)))))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) x)))
	90.8%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) tau) (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	85.1%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
	79.7%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (*.f32 tau (PI.f32))))))
	79.6%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 x (.f32 x x))))) (*.f32 x (PI.f32))))))
	85.4%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 (/.f32 (fma.f32 (.f32 (.f32 x (.f32 (PI.f32) #s(literal -1/6 binary32))) x) (.f32 (PI.f32) tau) tau) (.f32 tau (.f32 (PI.f32) tau))) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	85.6%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 #s(approx (+ (* x (* x (/ (* -1/6 (PI)) tau))) (/ 1 (* tau (PI)))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) tau)) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	71.1%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 #s(approx (+ (* x (* x (/ (* -1/6 (PI)) tau))) (/ 1 (* tau (PI)))) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	71.1%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	85.3%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) #s(approx (/ (+ (* x (* x (/ (* -1/6 (PI)) tau))) (/ 1 (* tau (PI)))) x) (fma.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau) (/.f32 x (.f32 (.f32 x x) (.f32 tau (PI.f32))))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	85.7%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) #s(approx (/ (+ (* x (* x (/ (* -1/6 (PI)) tau))) (/ 1 (* tau (PI)))) x) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 x tau)))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	85.3%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (* (PI) tau) x)))) #s(approx (/ (+ (* x (* x (/ (* -1/6 (PI)) tau))) (/ 1 (* tau (PI)))) x) (.f32 (fma.f32 (/.f32 (PI.f32) tau) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (.f32 x x) (.f32 tau (PI.f32))))) (neg.f32 x)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	79.7%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) x) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
	85.7%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x 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)))
	65.0%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* (PI) (* x tau)))) (sin (* x (PI)))) x) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	79.7%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (* (PI) (* (PI) tau))) (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)))
✓	64.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 8 143 to 2 508 computations (69.2% saved)

regimes225.0ms (1.5%)

Memory

20.2MiB live, 361.9MiB allocated

Counts

192 → 1

Calls

Call 1

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

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

Calls

4 calls:

55.0ms	tau
54.0ms	x
54.0ms	(*.f32 x (PI.f32))
52.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes219.0ms (1.5%)

Memory

27.3MiB live, 266.7MiB allocated

Counts

143 → 1

Calls

Call 1

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

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

Calls

4 calls:

82.0ms	(.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))))
48.0ms	(*.f32 x (PI.f32))
44.0ms	x
39.0ms	tau

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes165.0ms (1.1%)

Memory

-0.5MiB live, 307.0MiB allocated

Counts

141 → 1

Calls

Call 1

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

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:

41.0ms	(.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
39.0ms	tau
38.0ms	(*.f32 x (PI.f32))

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes194.0ms (1.3%)

Memory

1.1MiB live, 232.0MiB allocated

Counts

132 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

61.0ms	(*.f32 x (PI.f32))
53.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
39.0ms	x
36.0ms	tau

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)

regimes155.0ms (1%)

Memory

17.0MiB live, 288.0MiB allocated

Counts

131 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

38.0ms	(*.f32 x (PI.f32))
37.0ms	tau
37.0ms	(.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))))
36.0ms	x

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes182.0ms (1.2%)

Memory

1.0MiB live, 315.1MiB allocated

Counts

130 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

60.0ms	(.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))))
39.0ms	tau
37.0ms	x
37.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
90.8%	1	`x`
90.8%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
90.8%	1	`(*.f32 x (PI.f32))`
90.8%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes166.0ms (1.1%)

Memory

15.8MiB live, 323.5MiB allocated

Counts

128 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

42.0ms	x
41.0ms	tau
39.0ms	(*.f32 x (PI.f32))
38.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
86.2%	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))))`
86.2%	1	`x`
86.2%	1	`(*.f32 x (PI.f32))`
86.2%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes69.0ms (0.5%)

Memory

27.2MiB live, 147.5MiB allocated

Counts

53 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

18.0ms	(*.f32 x (PI.f32))
17.0ms	x
17.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
15.0ms	tau

Results

Accuracy	Segments	Branch
86.2%	1	`x`
86.2%	1	`tau`
86.2%	1	`(*.f32 x (PI.f32))`
86.2%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes75.0ms (0.5%)

Memory

-29.0MiB live, 143.7MiB allocated

Counts

51 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

22.0ms	(*.f32 x (PI.f32))
17.0ms	tau
17.0ms	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))))

Results

Accuracy	Segments	Branch
86.2%	1	`x`
86.2%	1	`(*.f32 x (PI.f32))`
86.2%	1	`tau`
86.2%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes83.0ms (0.6%)

Memory

-5.3MiB live, 113.8MiB allocated

Counts

47 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

36.0ms	x
16.0ms	(*.f32 x (PI.f32))
16.0ms	(.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
80.4%	1	`x`
80.4%	1	`tau`
80.4%	1	`(*.f32 x (PI.f32))`
80.4%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes48.0ms (0.3%)

Memory

1.0MiB live, 38.2MiB allocated

Counts

19 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

29.0ms	(*.f32 x (PI.f32))
6.0ms	tau
6.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
6.0ms	x

Results

Accuracy	Segments	Branch
80.4%	1	`x`
80.4%	1	`(*.f32 x (PI.f32))`
80.4%	1	`tau`
80.4%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes27.0ms (0.2%)

Memory

13.2MiB live, 50.4MiB allocated

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

9.0ms	(*.f32 x (PI.f32))
6.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
6.0ms	tau
6.0ms	x

Results

Accuracy	Segments	Branch
79.7%	1	`x`
79.7%	1	`(*.f32 x (PI.f32))`
79.7%	1	`tau`
79.7%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes20.0ms (0.1%)

Memory

1.8MiB live, 39.4MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (*.f32 x x) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 x (.f32 x #s(literal -1/6 binary32))) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) x))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) x) (*.f32 (PI.f32) x)) #s(literal -1/6 binary32) #s(literal 1 binary32))))
(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (PI.f32) (.f32 x tau)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (* (PI) (* (PI) tau))) (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))
4.0ms	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
79.7%	1	`x`
79.7%	1	`tau`
79.7%	1	`(*.f32 x (PI.f32))`
79.7%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes19.0ms (0.1%)

Memory

-10.3MiB live, 33.2MiB 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))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (*.f32 x x) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 x (.f32 x #s(literal -1/6 binary32))) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) x))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* (PI) tau) x)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) x) (*.f32 (PI.f32) x)) #s(literal -1/6 binary32) #s(literal 1 binary32))))
(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (PI.f32) (.f32 x tau)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) tau)))

Outputs

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

Calls

4 calls:

7.0ms	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
65.1%	1	`x`
65.1%	1	`tau`
65.1%	1	`(*.f32 x (PI.f32))`
65.1%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes15.0ms (0.1%)

Memory

-9.6MiB live, 28.0MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
65.1%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
65.1%	1	`tau`
65.1%	1	`x`
65.1%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes7.0ms (0%)

Memory

17.0MiB live, 17.0MiB allocated

Accuracy

Total -19.4b remaining (-169.6%)

Threshold costs -19.4b (-169.6%)

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))

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
64.2%	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))))`
64.2%	1	`tau`
64.2%	1	`x`
64.2%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

simplify13.0ms (0.1%)

Memory

-15.2MiB live, 21.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	122	570
1	168	570

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.4s (16.2%)

Memory

-4.8MiB live, 1 566.5MiB allocated

Rules

24 526×	`lower-fma.f64`
24 526×	`lower-fma.f32`
17 258×	`lower-fma.f64`
17 258×	`lower-fma.f32`
16 966×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	289
0	86	285
1	274	285
2	1495	273
0	8431	271
0	196	1582
1	620	1562
2	2413	1538
3	4145	1538
4	4880	1538
5	5560	1538
6	5950	1538
7	5981	1538
8	5981	1538
0	8826	1486
0	40	220
0	71	222
1	240	212
2	1420	198
3	7834	198
0	8005	198
0	440	7051
1	1456	6895
2	5517	6691
0	8386	6440
0	375	6502
1	1253	6337
2	4877	6148
0	8228	5948
0	10	55
0	18	55
1	63	55
2	483	53
3	6485	53
0	8114	53
0	52	343
0	89	343
1	323	343
2	1752	327
0	8447	321
0	397	7508
1	1323	7326
2	5149	7116
0	8144	6882

Stop Event

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

Compiler

Compiled 1 211 to 481 computations (60.3% saved)

preprocess86.0ms (0.6%)

Memory

40.6MiB live, 235.6MiB allocated

Remove

(abs x)

(abs tau)

Compiler

Compiled 2 004 to 788 computations (60.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze25.0ms (0.2%)

sample1.6s (10.9%)

preprocess77.0ms (0.5%)

explain205.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify34.0ms (0.2%)

localize39.0ms (0.3%)

series41.0ms (0.3%)

simplify622.0ms (4.2%)

rewrite350.0ms (2.4%)

eval145.0ms (1%)

prune391.0ms (2.6%)

simplify348.0ms (2.3%)

localize871.0ms (5.9%)

series159.0ms (1.1%)

simplify474.0ms (3.2%)

rewrite312.0ms (2.1%)

eval328.0ms (2.2%)

prune337.0ms (2.3%)

simplify125.0ms (0.8%)

localize156.0ms (1.1%)

series29.0ms (0.2%)

simplify543.0ms (3.7%)

rewrite426.0ms (2.9%)

eval385.0ms (2.6%)

prune600.0ms (4%)

simplify48.0ms (0.3%)

localize238.0ms (1.6%)

series24.0ms (0.2%)

simplify612.0ms (4.1%)

rewrite364.0ms (2.5%)

eval188.0ms (1.3%)

prune541.0ms (3.6%)

regimes225.0ms (1.5%)

regimes219.0ms (1.5%)

regimes165.0ms (1.1%)

regimes194.0ms (1.3%)

regimes155.0ms (1%)

regimes182.0ms (1.2%)

regimes166.0ms (1.1%)

regimes69.0ms (0.5%)

regimes75.0ms (0.5%)

regimes83.0ms (0.6%)

regimes48.0ms (0.3%)

regimes27.0ms (0.2%)

regimes20.0ms (0.1%)

regimes19.0ms (0.1%)

regimes15.0ms (0.1%)

regimes7.0ms (0%)

simplify13.0ms (0.1%)

soundness2.4s (16.2%)

preprocess86.0ms (0.6%)

end0.0ms (0%)

Profiling