Metrics for Lanczos kernel

analyze33.0ms (0.3%)

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 38 to 20 computations (47.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-div: 4.0ms (18.9% of total)

ival-mult: 4.0ms (18.9% of total)

ival-sin: 4.0ms (18.9% of total)

ival-<=: 4.0ms (18.9% of total)

...c/correct-round.rkt:119:19: 3.0ms (14.2% of total)

ival-pi: 1.0ms (4.7% of total)

ival-and: 1.0ms (4.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample2.1s (16.2%)

Results

1.7s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-sin: 599.0ms (43.8% of total)

ival-mult: 220.0ms (16.1% of total)

...c/correct-round.rkt:119:19: 170.0ms (12.4% of total)

ival-<=: 162.0ms (11.9% of total)

ival-div: 124.0ms (9.1% of total)

ival-pi: 53.0ms (3.9% of total)

ival-and: 27.0ms (2% of total)

const: 8.0ms (0.6% of total)

backward-pass: 3.0ms (0.2% of total)

Bogosity

preprocess84.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

892×	`fma-define`
834×	`associate-l`
792×	`fnmadd-define`
766×	`distribute-lft-neg-in`
754×	`distribute-frac-neg2`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	136
1	106	136
2	488	128
3	2592	110
4	5365	110
0	10	21
1	23	21
2	80	21
3	284	18
4	679	18
5	1059	18
6	1090	18
7	1090	18
0	1090	18

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

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

Outputs

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

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

Call 2

Inputs
(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
(* (/ (sin (* (* (neg x) (PI)) tau)) (* (* (neg x) (PI)) tau)) (/ (sin (* (neg x) (PI))) (* (neg x) (PI))))
(* (/ (sin (* (* x (PI)) (neg tau))) (* (* x (PI)) (neg tau))) (/ (sin (* x (PI))) (* x (PI))))
(neg (* (/ (sin (* (* (neg x) (PI)) tau)) (* (* (neg x) (PI)) tau)) (/ (sin (* (neg x) (PI))) (* (neg x) (PI)))))
(neg (* (/ (sin (* (* x (PI)) (neg tau))) (* (* x (PI)) (neg tau))) (/ (sin (* x (PI))) (* x (PI)))))
(* (/ (sin (* (* tau (PI)) x)) (* (* tau (PI)) x)) (/ (sin (* tau (PI))) (* tau (PI))))

Outputs
(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
(* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* tau (square (* x (PI))))))
(* (/ (sin (* (* (neg x) (PI)) tau)) (* (* (neg x) (PI)) tau)) (/ (sin (* (neg x) (PI))) (* (neg x) (PI))))
(* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* tau (square (* x (PI))))))
(* (/ (sin (* (* x (PI)) (neg tau))) (* (* x (PI)) (neg tau))) (/ (sin (* x (PI))) (* x (PI))))
(* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* tau (square (* x (PI))))))
(neg (* (/ (sin (* (* (neg x) (PI)) tau)) (* (* (neg x) (PI)) tau)) (/ (sin (* (neg x) (PI))) (* (neg x) (PI)))))
(* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* tau (neg (square (* x (PI)))))))
(neg (* (/ (sin (* (* x (PI)) (neg tau))) (* (* x (PI)) (neg tau))) (/ (sin (* x (PI))) (* x (PI)))))
(* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* tau (neg (square (* x (PI)))))))
(* (/ (sin (* (* tau (PI)) x)) (* (* tau (PI)) x)) (/ (sin (* tau (PI))) (* tau (PI))))
(* (/ (sin (* (PI) (* x tau))) x) (/ (sin (* (PI) tau)) (square (* (PI) tau))))

Symmetry

(abs x)

(abs tau)

explain131.0ms (1%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
2	-	2	(0.42874154448509216 2.2916297912597656)	`(sin.f32 (.f32 (.f32 x (PI.f32)) tau))`
0	-	0	-	`x`
0	-	0	-	`tau`
0	-	0	-	`(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))`
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	-	`(sin.f32 (*.f32 x (PI.f32)))`
0	-	0	-	`(*.f32 x (PI.f32))`
0	-	0	-	`(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))`
0	-	0	-	`(PI.f32)`
0	-	0	-	`(.f32 (.f32 x (PI.f32)) tau)`

Results

87.0ms

512×

valid

Compiler

Compiled 153 to 32 computations (79.1% saved)

Precisions

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

ival-sin: 15.0ms (40.2% of total)

ival-mult: 13.0ms (34.8% of total)

ival-div: 7.0ms (18.7% of total)

ival-pi: 2.0ms (5.4% of total)

const: 1.0ms (2.7% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 23 to 12 computations (47.8% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.3%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
▶	98.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Status

Accuracy

Program

▶

97.3%

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

▶

98.0%

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

Compiler

Compiled 46 to 22 computations (52.2% saved)

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

672×	`times-frac`
578×	`-lowering-.f32`
578×	`-lowering-.f64`
548×	`associate-/r*`
540×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	134
1	48	134
2	156	125
3	571	124
4	1117	124
5	1200	124
6	1200	124
0	1200	124

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize139.0ms (1.1%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.9%	(.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))
✓	accuracy	98.8%	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))
✓	accuracy	98.7%	(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
✓	accuracy	98.7%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
✓	accuracy	99.0%	(*.f32 x (PI.f32))
✓	accuracy	98.7%	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
✓	accuracy	98.7%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	accuracy	98.6%	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

Results

114.0ms

256×

valid

Compiler

Compiled 137 to 18 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-div: 31.0ms (41.1% of total)

ival-sin: 27.0ms (35.8% of total)

ival-mult: 15.0ms (19.9% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series34.0ms (0.3%)

Counts

11 → 240

Calls

Call 1

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

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 (* (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 (* 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))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>

Calls

60 calls:

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

rewrite362.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

5240×	`-lowering-.f32`
5240×	`-lowering-.f64`
3704×	`/-lowering-/.f32`
3704×	`/-lowering-/.f64`
1578×	`sum5-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	105
1	101	105
2	778	98
3	7573	98
0	8437	98

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 878

Calls

Call 1

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

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

simplify285.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

5212×	`-lowering-.f32`
5212×	`-lowering-.f64`
5120×	`+-lowering-+.f64`
5120×	`+-lowering-+.f32`
1244×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	3255
1	931	2974
2	4084	2860
0	8093	2860

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

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 (* (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))))
(* 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))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))

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

eval127.0ms (1%)

Compiler: Compiled 36599 to 2588 computations (92.9% saved)

prune268.0ms (2.1%)

Pruning

37 alts after pruning (36 fresh and 1 done)

	Pruned	Kept	Total
New	1430	36	1466
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	1431	37	1468

Accuracy

99.9%

Counts

1468 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.7%	(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 x (sin.f32 (.f32 (PI.f32) (.f32 x tau))))) x) (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
	68.3%	(/.f32 (/.f32 (-.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32)))))))) (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))))))) (.f32 #s(literal 2 binary32) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
▶	66.9%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (.f32 x (PI.f32)) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))) tau)
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 x (sin.f32 (.f32 x (PI.f32)))))
	97.4%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) tau)) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) x))
▶	97.5%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (/.f32 tau (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
▶	97.9%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
	97.3%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (PI.f32))))
	66.8%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))))) #s(literal 2 binary32))
	66.8%	(/.f32 (-.f32 (pow.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) #s(literal 3 binary32)) (pow.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))) #s(literal 3 binary32))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #s(literal 2 binary32))) (+.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32)))))))) (.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (*.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))))))))
	65.1%	(/.f32 (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	96.8%	(/.f32 (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 x (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
	95.8%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32)) (.f32 x tau)))))
	96.7%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 x tau)) (PI.f32))))
✓	97.3%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	96.8%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
▶	81.7%	(/.f32 (.f32 tau (.f32 (sin.f32 (.f32 x (PI.f32))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	96.3%	(/.f32 (.f32 #s(literal -2 binary32) (/.f32 (.f32 (sin.f32 (/.f32 (.f32 x (-.f32 (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32))) (sin.f32 (/.f32 (.f32 x (+.f32 (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32)))) #s(literal 2 binary32))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	97.7%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 x (PI.f32)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))))
	66.2%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
	73.7%	(-.f32 (/.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (/.f32 (/.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))) #s(literal 2 binary32)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))))
	87.1%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (+.f32 #s(literal 1/120 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32)))))))))
	82.4%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))))))
	97.4%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) tau) (PI.f32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	82.0%	(.f32 (/.f32 (.f32 x (+.f32 (.f32 tau (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 1/3 binary32))) tau))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 1/3 binary32))) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (*.f32 x (pow.f32 (PI.f32) #s(literal 1/3 binary32)))))))
	87.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))))))
	72.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (*.f32 x (PI.f32)) tau)) #s(literal 1 binary32))
	66.8%	(.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (/.f32 #s(literal 1/2 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))))
	82.7%	(.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	65.4%	#s(literal 1 binary32)

Compiler

Compiled 2115 to 1166 computations (44.9% saved)

simplify486.0ms (3.8%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32)))))
✓	cost-diff	0	(-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))))
✓	cost-diff	0	(/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
✓	cost-diff	0	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
✓	cost-diff	0	(.f32 (PI.f32) (.f32 x tau))
✓	cost-diff	0	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	cost-diff	0	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x tau))))
✓	cost-diff	0	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
✓	cost-diff	64	(+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))))
✓	cost-diff	64	(.f32 (sin.f32 (.f32 x (PI.f32))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))
✓	cost-diff	64	(.f32 tau (.f32 (sin.f32 (.f32 x (PI.f32))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))))))
✓	cost-diff	192	(/.f32 (.f32 tau (.f32 (sin.f32 (.f32 x (PI.f32))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
✓	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 (PI.f32) (*.f32 x tau)))
✓	cost-diff	0	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))

Rules

5244×	`-lowering-.f32`
5244×	`-lowering-.f64`
2864×	`/-lowering-/.f32`
2864×	`/-lowering-/.f64`
2180×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	445
1	148	435
2	560	416
3	3317	410
4	4195	398
5	5720	398
0	8112	398

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ (sin (* x (PI))) (* (PI) (* x tau))) (/ (* x (PI)) (sin (* (PI) (* x tau)))))
(/ (sin (* x (PI))) (* (PI) (* x tau)))
(sin (* x (PI)))
(* x (PI))
x
(PI)
(* (PI) (* x tau))
(* x tau)
tau
(/ (* x (PI)) (sin (* (PI) (* x tau))))
(sin (* (PI) (* x tau)))
1
(/ (* tau (* (sin (* x (PI))) (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6))))) (* x (* (PI) (* x (* (PI) tau)))))
(* tau (* (sin (* x (PI))) (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6)))))
tau
(* (sin (* x (PI))) (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6))))
(sin (* x (PI)))
(* x (PI))
x
(PI)
(+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6)))
(* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6))
(* tau (* tau (* x (* x x))))
(* tau (* x (* x x)))
(* x (* x x))
(* x x)
(* (* (PI) (* (PI) (PI))) -1/6)
(* (PI) (* (PI) (PI)))
(* (PI) (PI))
-1/6
(* x (* (PI) (* x (* (PI) tau))))
(* (PI) (* x (* (PI) tau)))
(* x (* (PI) tau))
(* (PI) tau)
(/ (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* x tau)))) (/ (PI) (sin (* x (PI)))))
(/ (sin (* (PI) (* x tau))) (* x (* (PI) (* x tau))))
(sin (* (PI) (* x tau)))
(* (PI) (* x tau))
(PI)
(* x tau)
x
tau
(* x (* (PI) (* x tau)))
(/ (PI) (sin (* x (PI))))
(sin (* x (PI)))
(* x (PI))
(/ (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* x (PI)) (+ tau 1)))) (* x (* (PI) (* (PI) (* x tau))))) 2)
(/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* x (PI)) (+ tau 1)))) (* x (* (PI) (* (PI) (* x tau)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (* x (PI)) (+ tau 1))))
(cos (* x (* (PI) (- tau 1))))
(* x (* (PI) (- tau 1)))
x
(* (PI) (- tau 1))
(PI)
(- tau 1)
tau
1
(cos (* (* x (PI)) (+ tau 1)))
(* (* x (PI)) (+ tau 1))
(* x (PI))
(+ tau 1)
(* x (* (PI) (* (PI) (* x tau))))
(* (PI) (* (PI) (* x tau)))
(* (PI) (* x tau))
(* x tau)
2

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

localize302.0ms (2.4%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))
✓	accuracy	98.7%	(/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
✓	accuracy	98.7%	(.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))
✓	accuracy	67.9%	(-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))))
✓	accuracy	98.8%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.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))
✓	accuracy	98.6%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
✓	accuracy	98.7%	(.f32 (sin.f32 (.f32 x (PI.f32))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))
✓	accuracy	98.6%	(/.f32 (.f32 tau (.f32 (sin.f32 (.f32 x (PI.f32))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
✓	accuracy	96.9%	(.f32 (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	98.8%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
✓	accuracy	98.8%	(/.f32 (sin.f32 (.f32 x (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))

Results

218.0ms

256×

valid

Compiler

Compiled 491 to 47 computations (90.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 111.0ms

ival-mult: 41.0ms (37.1% of total)

ival-sub: 24.0ms (21.7% of total)

ival-div: 17.0ms (15.4% of total)

ival-sin: 10.0ms (9% of total)

ival-cos: 9.0ms (8.1% of total)

...c/correct-round.rkt:119:19: 4.0ms (3.6% of total)

ival-add: 3.0ms (2.7% of total)

ival-pi: 1.0ms (0.9% of total)

const: 1.0ms (0.9% of total)

backward-pass: 0.0ms (0% of total)

series100.0ms (0.8%)

Counts

19 → 384

Calls

Call 1

Inputs
#<alt (/ (/ (sin (* x (PI))) (* (PI) (* x tau))) (/ (* x (PI)) (sin (* (PI) (* x tau)))))>
#<alt (/ (sin (* x (PI))) (* (PI) (* x tau)))>
#<alt (sin (* x (PI)))>
#<alt (* x (PI))>
#<alt (/ (* tau (* (sin (* x (PI))) (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6))))) (* x (* (PI) (* x (* (PI) tau)))))>
#<alt (* tau (* (sin (* x (PI))) (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6)))))>
#<alt (* (sin (* x (PI))) (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6))))>
#<alt (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6)))>
#<alt (/ (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* x tau)))) (/ (PI) (sin (* x (PI)))))>
#<alt (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* x tau))))>
#<alt (sin (* (PI) (* x tau)))>
#<alt (* (PI) (* x tau))>
#<alt (/ (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* x (PI)) (+ tau 1)))) (* x (* (PI) (* (PI) (* x tau))))) 2)>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* x (PI)) (+ tau 1)))) (* x (* (PI) (* (PI) (* x tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* x (PI)) (+ tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (* (PI) (PI))>
#<alt (* (* (PI) (* (PI) (PI))) -1/6)>
#<alt (* (* x (PI)) (+ tau 1))>

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 tau)>
#<alt (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) tau)) (/ 1 tau))>
#<alt (+ (* (pow x 2) (+ (* -1/6 (/ (pow (PI) 2) tau)) (* 1/120 (/ (* (pow x 2) (pow (PI) 4)) tau)))) (/ 1 tau))>
#<alt (+ (* (pow x 2) (+ (* -1/6 (/ (pow (PI) 2) tau)) (* (pow x 2) (+ (* -1/5040 (/ (* (pow x 2) (pow (PI) 6)) tau)) (* 1/120 (/ (pow (PI) 4) tau)))))) (/ 1 tau))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* x (PI))))>
#<alt (/ (sin (* x (PI))) (* tau (* 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 (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
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#<alt (+ (* 1/2 (* (pow x 2) (- (* 1/24 (/ (* (pow (PI) 2) (pow (- tau 1) 4)) tau)) (* 1/24 (/ (* (pow (PI) 2) (pow (+ 1 tau) 4)) tau))))) (* 1/2 (/ (- (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))) (* tau (pow (PI) 2)))))>
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#<alt (+ (* 1/2 (/ (- (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))) (* tau (pow (PI) 2)))) (* (pow x 2) (+ (* 1/2 (- (* 1/24 (/ (* (pow (PI) 2) (pow (- tau 1) 4)) tau)) (* 1/24 (/ (* (pow (PI) 2) (pow (+ 1 tau) 4)) tau)))) (* (pow x 2) (+ (* 1/2 (* (pow x 2) (- (* 1/40320 (/ (* (pow (PI) 6) (pow (- tau 1) 8)) tau)) (* 1/40320 (/ (* (pow (PI) 6) (pow (+ 1 tau) 8)) tau))))) (* 1/2 (- (* -1/720 (/ (* (pow (PI) 4) (pow (- tau 1) 6)) tau)) (* -1/720 (/ (* (pow (PI) 4) (pow (+ 1 tau) 6)) tau)))))))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (/ (+ (* 1/2 (* tau (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI)))))) (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2))))) tau)>
#<alt (/ (+ (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (* tau (+ (* 1/2 (* tau (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI))))))) (* 1/2 (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI)))))))) tau)>
#<alt (/ (+ (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (* tau (+ (* 1/2 (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI))))) (* tau (+ (* 1/2 (* tau (- (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* -1/6 (* x (* (PI) (sin (* -1 (* x (PI)))))))))) (* 1/2 (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI))))))))))) tau)>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau)))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau)))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau)))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (* 1/2 (/ (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau)))))) (* tau (* (pow x 2) (pow (PI) 2)))))>
#<alt (/ (- (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))) (* tau (pow (PI) 2)))>
#<alt (- (+ (* -1/2 (/ (pow (- tau 1) 2) tau)) (* (pow x 2) (- (* 1/24 (/ (* (pow (PI) 2) (pow (- tau 1) 4)) tau)) (* 1/24 (/ (* (pow (PI) 2) (pow (+ 1 tau) 4)) tau))))) (* -1/2 (/ (pow (+ 1 tau) 2) tau)))>
#<alt (- (+ (* -1/2 (/ (pow (- tau 1) 2) tau)) (* (pow x 2) (- (+ (* 1/24 (/ (* (pow (PI) 2) (pow (- tau 1) 4)) tau)) (* (pow x 2) (- (* -1/720 (/ (* (pow (PI) 4) (pow (- tau 1) 6)) tau)) (* -1/720 (/ (* (pow (PI) 4) (pow (+ 1 tau) 6)) tau))))) (* 1/24 (/ (* (pow (PI) 2) (pow (+ 1 tau) 4)) tau))))) (* -1/2 (/ (pow (+ 1 tau) 2) tau)))>
#<alt (- (+ (* -1/2 (/ (pow (- tau 1) 2) tau)) (* (pow x 2) (- (+ (* 1/24 (/ (* (pow (PI) 2) (pow (- tau 1) 4)) tau)) (* (pow x 2) (- (+ (* -1/720 (/ (* (pow (PI) 4) (pow (- tau 1) 6)) tau)) (* (pow x 2) (- (* 1/40320 (/ (* (pow (PI) 6) (pow (- tau 1) 8)) tau)) (* 1/40320 (/ (* (pow (PI) 6) (pow (+ 1 tau) 8)) tau))))) (* -1/720 (/ (* (pow (PI) 4) (pow (+ 1 tau) 6)) tau))))) (* 1/24 (/ (* (pow (PI) 2) (pow (+ 1 tau) 4)) tau))))) (* -1/2 (/ (pow (+ 1 tau) 2) tau)))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (+ (* tau (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI))))) (/ (cos (* -1 (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (/ (cos (* x (PI))) (* (pow x 2) (pow (PI) 2)))) tau)>
#<alt (/ (- (+ (* tau (- (+ (* tau (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI)))))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* -1 (* x (PI)))) (* x (PI))))) (/ (cos (* -1 (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (/ (cos (* x (PI))) (* (pow x 2) (pow (PI) 2)))) tau)>
#<alt (/ (- (+ (* tau (- (+ (* tau (- (+ (* -1/2 (cos (* -1 (* x (PI))))) (* tau (- (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* -1/6 (* x (* (PI) (sin (* -1 (* x (PI)))))))))) (* -1/2 (cos (* x (PI)))))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* -1 (* x (PI)))) (* x (PI))))) (/ (cos (* -1 (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (/ (cos (* x (PI))) (* (pow x 2) (pow (PI) 2)))) tau)>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau)))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau)))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau)))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (/ (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau)))))) (* tau (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow x 2) (- (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (+ (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* (pow x 2) (- (* -1/720 (* (pow (PI) 6) (pow (- tau 1) 6))) (* -1/720 (* (pow (PI) 6) (pow (+ 1 tau) 6)))))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (+ (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* (pow x 2) (- (+ (* -1/720 (* (pow (PI) 6) (pow (- tau 1) 6))) (* (pow x 2) (- (* 1/40320 (* (pow (PI) 8) (pow (- tau 1) 8))) (* 1/40320 (* (pow (PI) 8) (pow (+ 1 tau) 8)))))) (* -1/720 (* (pow (PI) 6) (pow (+ 1 tau) 6)))))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* -1 (* x (PI)))) (cos (* x (PI))))>
#<alt (- (+ (cos (* -1 (* x (PI)))) (* tau (- (* x (* (PI) (sin (* x (PI))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI))))>
#<alt (- (+ (cos (* -1 (* x (PI)))) (* tau (- (+ (* tau (- (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* x (PI)))))))) (* x (* (PI) (sin (* x (PI)))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI))))>
#<alt (- (+ (cos (* -1 (* x (PI)))) (* tau (- (+ (* tau (- (+ (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* tau (- (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))) (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI)))))))))) (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* x (PI)))))))) (* x (* (PI) (sin (* x (PI)))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))>
#<alt (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))>
#<alt (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))>
#<alt (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* (pow x 2) (* (pow (PI) 2) (pow (- tau 1) 2)))))>
#<alt (+ 1 (* (pow x 2) (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* 1/24 (* (pow x 2) (* (pow (PI) 4) (pow (- tau 1) 4)))))))>
#<alt (+ 1 (* (pow x 2) (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (* (pow (PI) 6) (pow (- tau 1) 6)))) (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))))))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* -1 (* x (PI))))>
#<alt (+ (cos (* -1 (* x (PI)))) (* -1 (* tau (* x (* (PI) (sin (* -1 (* x (PI)))))))))>
#<alt (+ (cos (* -1 (* x (PI)))) (* tau (- (* -1/2 (* tau (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI)))))))) (* x (* (PI) (sin (* -1 (* x (PI)))))))))>
#<alt (+ (cos (* -1 (* x (PI)))) (* tau (- (* tau (+ (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* 1/6 (* tau (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI)))))))))) (* x (* (PI) (sin (* -1 (* x (PI)))))))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))>
#<alt (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))>
#<alt (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))>
#<alt (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (* (PI) (+ 1 tau)))>
#<alt (* x (PI))>
#<alt (+ (* tau (* x (PI))) (* x (PI)))>
#<alt (+ (* tau (* x (PI))) (* x (PI)))>
#<alt (+ (* tau (* x (PI))) (* x (PI)))>
#<alt (* tau (* x (PI)))>
#<alt (* tau (+ (* x (PI)) (/ (* x (PI)) tau)))>
#<alt (* tau (+ (* x (PI)) (/ (* x (PI)) tau)))>
#<alt (* tau (+ (* x (PI)) (/ (* x (PI)) tau)))>
#<alt (* tau (* x (PI)))>
#<alt (* -1 (* tau (+ (* -1 (* x (PI))) (* -1 (/ (* x (PI)) tau)))))>
#<alt (* -1 (* tau (+ (* -1 (* x (PI))) (* -1 (/ (* x (PI)) tau)))))>
#<alt (* -1 (* tau (+ (* -1 (* x (PI))) (* -1 (/ (* x (PI)) tau)))))>

Calls

96 calls:

Time	Variable		Point	Expression
48.0ms	tau	@	-inf	(sin (* (PI) (* x tau)))
7.0ms	tau	@	0	(/ (sin (* (PI) (* x tau))) (* x (* (PI) (* x tau))))
6.0ms	tau	@	inf	(/ (sin (* x (PI))) (* (PI) (* x tau)))
2.0ms	x	@	0	(/ (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* x (PI)) (+ tau 1)))) (* x (* (PI) (* (PI) (* x tau))))) 2)
2.0ms	x	@	inf	(/ (* tau (* (sin (* x (PI))) (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6))))) (* x (* (PI) (* x (* (PI) tau)))))

rewrite548.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

4156×	`-lowering-.f32`
4156×	`-lowering-.f64`
4056×	`/-lowering-/.f32`
4056×	`/-lowering-/.f64`
1446×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	269
1	279	244
2	2382	233
0	8468	233

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 836

Calls

Call 1

Inputs
(/ (/ (sin (* x (PI))) (* (PI) (* x tau))) (/ (* x (PI)) (sin (* (PI) (* x tau)))))
(/ (sin (* x (PI))) (* (PI) (* x tau)))
(sin (* x (PI)))
(* x (PI))
(/ (* tau (* (sin (* x (PI))) (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6))))) (* x (* (PI) (* x (* (PI) tau)))))
(* tau (* (sin (* x (PI))) (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6)))))
(* (sin (* x (PI))) (+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6))))
(+ (* x (PI)) (* (* tau (* tau (* x (* x x)))) (* (* (PI) (* (PI) (PI))) -1/6)))
(/ (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* x tau)))) (/ (PI) (sin (* x (PI)))))
(/ (sin (* (PI) (* x tau))) (* x (* (PI) (* x tau))))
(sin (* (PI) (* x tau)))
(* (PI) (* x tau))
(/ (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* x (PI)) (+ tau 1)))) (* x (* (PI) (* (PI) (* x tau))))) 2)
(/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* x (PI)) (+ tau 1)))) (* x (* (PI) (* (PI) (* x tau)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (* x (PI)) (+ tau 1))))
(cos (* x (* (PI) (- tau 1))))
(* (PI) (PI))
(* (* (PI) (* (PI) (PI))) -1/6)
(* (* x (PI)) (+ tau 1))

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

simplify480.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

5200×	`-lowering-.f32`
5200×	`-lowering-.f64`
3658×	`+-lowering-+.f64`
3658×	`+-lowering-+.f32`
1982×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	626	7880
1	2262	6993
2	6359	6883
0	8499	6883

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

Inputs
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
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(* x (PI))
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(- (+ (cos (* -1 (* x (PI)))) (* tau (- (* x (* (PI) (sin (* x (PI))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI))))
(+.f32 (.f32 tau (.f32 (.f32 x (PI.f32)) (-.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))))))) (-.f32 (cos.f32 (.f32 x (PI.f32))) (cos.f32 (*.f32 x (PI.f32)))))
(- (+ (cos (* -1 (* x (PI)))) (* tau (- (+ (* tau (- (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* x (PI)))))))) (* x (* (PI) (sin (* x (PI)))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI))))
(+.f32 (cos.f32 (.f32 x (PI.f32))) (-.f32 (.f32 tau (+.f32 (.f32 (.f32 x (PI.f32)) (-.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32)))))) (.f32 tau (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))) (-.f32 (cos.f32 (.f32 x (PI.f32))) (cos.f32 (.f32 x (PI.f32))))))))) (cos.f32 (*.f32 x (PI.f32)))))
(- (+ (cos (* -1 (* x (PI)))) (* tau (- (+ (* tau (- (+ (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* tau (- (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))) (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI)))))))))) (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* x (PI)))))))) (* x (* (PI) (sin (* x (PI)))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI))))
(+.f32 (.f32 tau (+.f32 (.f32 (.f32 x (PI.f32)) (-.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32)))))) (.f32 tau (+.f32 (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 x (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (-.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32)))))))) (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))) (-.f32 (cos.f32 (.f32 x (PI.f32))) (cos.f32 (.f32 x (PI.f32)))))))))) (-.f32 (cos.f32 (.f32 x (PI.f32))) (cos.f32 (*.f32 x (PI.f32)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))
(-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))
(-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))
(-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))
(-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))))
(- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))
(-.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))))
(- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))
(-.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))))
(- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))
(-.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))))
(- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))
(-.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))))
1
#s(literal 1 binary32)
(+ 1 (* -1/2 (* (pow x 2) (* (pow (PI) 2) (pow (- tau 1) 2)))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))))))
(+ 1 (* (pow x 2) (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* 1/24 (* (pow x 2) (* (pow (PI) 4) (pow (- tau 1) 4)))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32)))) (.f32 (.f32 #s(literal 1/24 binary32) (.f32 x x)) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (pow.f32 (+.f32 tau #s(literal -1 binary32)) #s(literal 4 binary32)))))))
(+ 1 (* (pow x 2) (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (* (pow (PI) 6) (pow (- tau 1) 6)))) (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32)))) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 #s(literal 1/24 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32))) (pow.f32 (+.f32 tau #s(literal -1 binary32)) #s(literal 4 binary32))) (.f32 #s(literal -1/720 binary32) (.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (pow.f32 (+.f32 tau #s(literal -1 binary32)) #s(literal 6 binary32))))))))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* -1 (* x (PI))))
(cos.f32 (*.f32 x (PI.f32)))
(+ (cos (* -1 (* x (PI)))) (* -1 (* tau (* x (* (PI) (sin (* -1 (* x (PI)))))))))
(-.f32 (cos.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (.f32 x (PI.f32)) (sin.f32 (-.f32 #s(literal 0 binary32) (*.f32 x (PI.f32)))))))
(+ (cos (* -1 (* x (PI)))) (* tau (- (* -1/2 (* tau (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI)))))))) (* x (* (PI) (sin (* -1 (* x (PI)))))))))
(+.f32 (cos.f32 (.f32 x (PI.f32))) (.f32 tau (-.f32 (.f32 (.f32 #s(literal -1/2 binary32) tau) (.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))) (cos.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) (sin.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))))))))
(+ (cos (* -1 (* x (PI)))) (* tau (- (* tau (+ (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* 1/6 (* tau (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI)))))))))) (* x (* (PI) (sin (* -1 (* x (PI)))))))))
(+.f32 (cos.f32 (.f32 x (PI.f32))) (.f32 tau (-.f32 (.f32 tau (+.f32 (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))) (cos.f32 (.f32 x (PI.f32))))) (.f32 (.f32 #s(literal 1/6 binary32) tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (sin.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))))))))) (.f32 (.f32 x (PI.f32)) (sin.f32 (-.f32 #s(literal 0 binary32) (*.f32 x (PI.f32))))))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))
(cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))
(cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau)))
(cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))
(cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau)))
(cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))
(cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau)))
(cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))
(cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (* (PI) (+ 1 tau)))
(.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau)))
(* x (PI))
(*.f32 x (PI.f32))
(+ (* tau (* x (PI))) (* x (PI)))
(.f32 (+.f32 #s(literal 1 binary32) tau) (.f32 x (PI.f32)))
(+ (* tau (* x (PI))) (* x (PI)))
(.f32 (+.f32 #s(literal 1 binary32) tau) (.f32 x (PI.f32)))
(+ (* tau (* x (PI))) (* x (PI)))
(.f32 (+.f32 #s(literal 1 binary32) tau) (.f32 x (PI.f32)))
(* tau (* x (PI)))
(.f32 tau (.f32 x (PI.f32)))
(* tau (+ (* x (PI)) (/ (* x (PI)) tau)))
(.f32 tau (.f32 x (+.f32 (PI.f32) (/.f32 (PI.f32) tau))))
(* tau (+ (* x (PI)) (/ (* x (PI)) tau)))
(.f32 tau (.f32 x (+.f32 (PI.f32) (/.f32 (PI.f32) tau))))
(* tau (+ (* x (PI)) (/ (* x (PI)) tau)))
(.f32 tau (.f32 x (+.f32 (PI.f32) (/.f32 (PI.f32) tau))))
(* tau (* x (PI)))
(.f32 tau (.f32 x (PI.f32)))
(* -1 (* tau (+ (* -1 (* x (PI))) (* -1 (/ (* x (PI)) tau)))))
(.f32 (neg.f32 tau) (neg.f32 (.f32 x (+.f32 (PI.f32) (/.f32 (PI.f32) tau)))))
(* -1 (* tau (+ (* -1 (* x (PI))) (* -1 (/ (* x (PI)) tau)))))
(.f32 (neg.f32 tau) (neg.f32 (.f32 x (+.f32 (PI.f32) (/.f32 (PI.f32) tau)))))
(* -1 (* tau (+ (* -1 (* x (PI))) (* -1 (/ (* x (PI)) tau)))))
(.f32 (neg.f32 tau) (neg.f32 (.f32 x (+.f32 (PI.f32) (/.f32 (PI.f32) tau)))))

eval185.0ms (1.4%)

Compiler: Compiled 54255 to 3684 computations (93.2% saved)

prune272.0ms (2.1%)

Pruning

50 alts after pruning (45 fresh and 5 done)

	Pruned	Kept	Total
New	1500	30	1530
Fresh	16	15	31
Picked	1	4	5
Done	0	1	1
Total	1517	50	1567

Accuracy

99.9%

Counts

1567 → 50

Alt Table

Click to see full alt table

Status	Accuracy	Program
	67.1%	(/.f32 (fma.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))) (neg.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))))) #s(literal 2 binary32))
	97.1%	(/.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (.f32 (PI.f32) tau)) x) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
	96.9%	(/.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (.f32 x tau)) (PI.f32)) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
	66.8%	(/.f32 (/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))) (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau)))) x) #s(literal 2 binary32))
	96.7%	(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 x (sin.f32 (.f32 (PI.f32) (.f32 x tau))))) x) (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
	66.9%	(/.f32 (/.f32 (-.f32 (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))))) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))))) (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))))) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	53.1%	(/.f32 (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32)))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	63.0%	(/.f32 (/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) x) (.f32 x (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))))) (*.f32 x x)) #s(literal 2 binary32))
	66.8%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau))))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
▶	66.8%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	66.9%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))) #s(literal 2 binary32))
	33.3%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	82.5%	(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) x) (/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32)))))
	65.1%	(/.f32 (/.f32 (.f32 (.f32 x x) (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau)))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))) #s(literal 2 binary32))
	87.4%	(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	65.2%	(/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau))))) (.f32 tau (*.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 x (sin.f32 (.f32 x (PI.f32)))))
	87.2%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))
	72.8%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (.f32 x (PI.f32))))
✓	97.5%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
▶	97.9%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (.f32 x (PI.f32)) tau))
	97.4%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (/.f32 tau (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
✓	97.9%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
	97.3%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (PI.f32))))
▶	97.3%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)))
	66.2%	(/.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32)))))
	72.9%	(/.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	74.6%	(/.f32 (-.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau)))) #s(literal 2 binary32))
▶	82.4%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
	87.1%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) tau) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (/.f32 (.f32 (PI.f32) (PI.f32)) tau)))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	65.1%	(/.f32 (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	96.8%	(/.f32 (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	95.8%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32)) (.f32 x tau)))))
✓	97.3%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	96.8%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
	81.5%	(/.f32 (.f32 tau (.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
	71.6%	(/.f32 (.f32 tau (.f32 (.f32 x (PI.f32)) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
✓	81.7%	(/.f32 (.f32 tau (.f32 (sin.f32 (.f32 x (PI.f32))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	81.7%	(/.f32 (.f32 tau (.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
	96.3%	(/.f32 (.f32 #s(literal -2 binary32) (/.f32 (.f32 (sin.f32 (/.f32 (.f32 x (-.f32 (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32))) (sin.f32 (/.f32 (.f32 x (+.f32 (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32)))) #s(literal 2 binary32))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	66.2%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
	87.1%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (+.f32 #s(literal 1/120 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32)))))))))
▶	82.4%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) #s(literal -1/6 binary32)))))
	96.9%	(.f32 (pow.f32 (/.f32 x (sin.f32 (.f32 x (PI.f32)))) #s(literal -1 binary32)) (pow.f32 (/.f32 (/.f32 (PI.f32) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau))) #s(literal -1 binary32)))
	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (*.f32 x (pow.f32 (PI.f32) #s(literal 1/3 binary32)))))))
	87.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))))))
	72.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (*.f32 x (PI.f32)) tau)) #s(literal 1 binary32))
	66.8%	(.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (/.f32 #s(literal 1/2 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))))
✓	65.4%	#s(literal 1 binary32)

Compiler

Compiled 2826 to 1600 computations (43.4% saved)

simplify337.0ms (2.6%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

4172×	`-lowering-.f32`
4172×	`-lowering-.f64`
3008×	`/-lowering-/.f32`
3008×	`/-lowering-/.f64`
2074×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	45	410
1	131	400
2	460	386
3	1703	383
4	3467	377
5	5722	377
0	8039	377

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ (sin (* x (PI))) (/ (* x (PI)) (sin (* (* x (PI)) tau)))) (* (* x (PI)) tau))
(/ (sin (* x (PI))) (/ (* x (PI)) (sin (* (* x (PI)) tau))))
(sin (* x (PI)))
(* x (PI))
x
(PI)
(/ (* x (PI)) (sin (* (* x (PI)) tau)))
(sin (* (* x (PI)) tau))
(* (* x (PI)) tau)
tau
(+ 1 (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))))
1
(* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)))
(* x x)
x
(* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))
(* (PI) (PI))
(PI)
(+ (* -1/6 (* tau tau)) -1/6)
(* -1/6 (* tau tau))
-1/6
(* tau tau)
tau
(/ (+ (/ 1 x) (* (* -1/6 (* tau tau)) (* x (* (PI) (PI))))) (/ (PI) (sin (* x (PI)))))
(+ (/ 1 x) (* (* -1/6 (* tau tau)) (* x (* (PI) (PI)))))
(/ 1 x)
1
x
(* (* -1/6 (* tau tau)) (* x (* (PI) (PI))))
(* -1/6 (* tau tau))
-1/6
(* tau tau)
tau
(* x (* (PI) (PI)))
(* (PI) (PI))
(PI)
(/ (PI) (sin (* x (PI))))
(sin (* x (PI)))
(* x (PI))
(/ (/ (sin (* x (PI))) (PI)) (* (/ (* x (PI)) (sin (* (* x (PI)) tau))) (* x tau)))
(/ (sin (* x (PI))) (PI))
(sin (* x (PI)))
(* x (PI))
x
(PI)
(* (/ (* x (PI)) (sin (* (* x (PI)) tau))) (* x tau))
(/ (* x (PI)) (sin (* (* x (PI)) tau)))
(sin (* (* x (PI)) tau))
(* (* x (PI)) tau)
tau
(* x tau)
(/ (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* (+ tau 1) x) (PI)))) (* x (* (PI) (* (PI) (* x tau))))) 2)
(/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* (+ tau 1) x) (PI)))) (* x (* (PI) (* (PI) (* x tau)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (* (+ tau 1) x) (PI))))
(cos (* x (* (PI) (- tau 1))))
(* x (* (PI) (- tau 1)))
x
(* (PI) (- tau 1))
(PI)
(- tau 1)
tau
1
(cos (* (* (+ tau 1) x) (PI)))
(* (* (+ tau 1) x) (PI))
(* (+ tau 1) x)
(+ tau 1)
(* x (* (PI) (* (PI) (* x tau))))
(* (PI) (* (PI) (* x tau)))
(* (PI) (* x tau))
(* x tau)
2

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

localize373.0ms (2.9%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.9%	(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
✓	accuracy	98.7%	(.f32 (PI.f32) (.f32 x tau))
✓	accuracy	98.7%	(/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
✓	accuracy	67.9%	(-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32))))
✓	accuracy	98.9%	(/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
✓	accuracy	98.9%	(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
✓	accuracy	98.8%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)))
✓	accuracy	98.7%	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
✓	accuracy	98.7%	(.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (*.f32 (PI.f32) (PI.f32))))
✓	accuracy	98.6%	(.f32 #s(literal -1/6 binary32) (.f32 tau tau))
✓	accuracy	98.6%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	99.0%	(.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) #s(literal -1/6 binary32))))
✓	accuracy	98.9%	(.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) #s(literal -1/6 binary32)))
✓	accuracy	98.6%	(.f32 #s(literal -1/6 binary32) (.f32 tau tau))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	99.0%	(*.f32 x (PI.f32))
✓	accuracy	98.9%	(/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
✓	accuracy	98.7%	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
✓	accuracy	98.6%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (.f32 x (PI.f32)) tau))

Results

233.0ms

256×

valid

Compiler

Compiled 447 to 46 computations (89.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-mult: 36.0ms (45% of total)

ival-div: 15.0ms (18.7% of total)

ival-sin: 8.0ms (10% of total)

ival-cos: 7.0ms (8.7% of total)

ival-add: 5.0ms (6.2% of total)

...c/correct-round.rkt:119:19: 4.0ms (5% of total)

ival-sub: 3.0ms (3.7% of total)

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

const: 1.0ms (1.2% of total)

backward-pass: 0.0ms (0% of total)

series37.0ms (0.3%)

Counts

24 → 468

Calls

Call 1

Inputs
#<alt (/ (/ (sin (* x (PI))) (/ (* x (PI)) (sin (* (* x (PI)) tau)))) (* (* x (PI)) tau))>
#<alt (/ (sin (* x (PI))) (/ (* x (PI)) (sin (* (* x (PI)) tau))))>
#<alt (sin (* x (PI)))>
#<alt (* x (PI))>
#<alt (+ 1 (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))))>
#<alt (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)))>
#<alt (* x x)>
#<alt (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))>
#<alt (/ (+ (/ 1 x) (* (* -1/6 (* tau tau)) (* x (* (PI) (PI))))) (/ (PI) (sin (* x (PI)))))>
#<alt (+ (/ 1 x) (* (* -1/6 (* tau tau)) (* x (* (PI) (PI)))))>
#<alt (/ 1 x)>
#<alt (* (* -1/6 (* tau tau)) (* x (* (PI) (PI))))>
#<alt (/ (/ (sin (* x (PI))) (PI)) (* (/ (* x (PI)) (sin (* (* x (PI)) tau))) (* x tau)))>
#<alt (/ (sin (* x (PI))) (PI))>
#<alt (/ (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* (+ tau 1) x) (PI)))) (* x (* (PI) (* (PI) (* x tau))))) 2)>
#<alt (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* (+ tau 1) x) (PI)))) (* x (* (PI) (* (PI) (* x tau)))))>
#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* (+ tau 1) x) (PI))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (sin (* (* x (PI)) tau))>
#<alt (/ (* x (PI)) (sin (* (* x (PI)) tau)))>
#<alt (* (PI) (PI))>
#<alt (* -1/6 (* tau tau))>
#<alt (* (PI) (* x tau))>
#<alt (* (PI) (* (PI) (* x tau)))>

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 (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (* -1/6 (* (pow tau 3) (pow (PI) 3)))))))>
#<alt (* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 5))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 5))) (* 1/36 (* (pow tau 3) (pow (PI) 5)))))))))))>
#<alt (* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 5))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 5))) (+ (* 1/36 (* (pow tau 3) (pow (PI) 5))) (* (pow x 2) (+ (* -1/720 (* (pow tau 3) (pow (PI) 7))) (+ (* -1/720 (* (pow tau 5) (pow (PI) 7))) (+ (* -1/5040 (* tau (pow (PI) 7))) (* -1/5040 (* (pow tau 7) (pow (PI) 7))))))))))))))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (* tau (sin (* x (PI))))>
#<alt (* tau (+ (sin (* x (PI))) (* -1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))))))>
#<alt (* tau (+ (sin (* x (PI))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI)))))))))))>
#<alt (* tau (+ (sin (* x (PI))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (* (pow (PI) 6) (sin (* x (PI))))))) (* 1/120 (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI))))))))))))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))>
#<alt (* 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) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6))))>
#<alt (+ 1 (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6))))>
#<alt (+ 1 (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6))))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))>
#<alt (+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))>
#<alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))>
#<alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))>
#<alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))>
#<alt (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))>
#<alt (* -1/6 (* (pow x 2) (pow (PI) 2)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2))))>
#<alt (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2))))>
#<alt (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2))))>
#<alt (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2)))))>
#<alt (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2)))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1/6 (pow (PI) 2))>
#<alt (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))>
#<alt (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))>
#<alt (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))>
#<alt (* -1/6 (* (pow tau 2) (pow (PI) 2)))>
#<alt (* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))>
#<alt (* -1/6 (* (pow tau 2) (pow (PI) 2)))>
#<alt (* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))>
#<alt (* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))>
#<alt 1>
#<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 (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 (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (* -1/5040 (pow (PI) 6)))))))))))>
#<alt (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI)))))))>
#<alt (* x (+ (* -1/6 (* (pow tau 2) (* (PI) (sin (* x (PI)))))) (/ (sin (* x (PI))) (* (pow x 2) (PI)))))>
#<alt (* x (+ (* -1/6 (* (pow tau 2) (* (PI) (sin (* x (PI)))))) (/ (sin (* x (PI))) (* (pow x 2) (PI)))))>
#<alt (* x (+ (* -1/6 (* (pow tau 2) (* (PI) (sin (* x (PI)))))) (/ (sin (* x (PI))) (* (pow x 2) (PI)))))>
#<alt (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI)))))))>
#<alt (* -1 (* x (+ (* -1 (/ (sin (* x (PI))) (* (pow x 2) (PI)))) (* 1/6 (* (pow tau 2) (* (PI) (sin (* x (PI)))))))))>
#<alt (* -1 (* x (+ (* -1 (/ (sin (* x (PI))) (* (pow x 2) (PI)))) (* 1/6 (* (pow tau 2) (* (PI) (sin (* x (PI)))))))))>
#<alt (* -1 (* x (+ (* -1 (/ (sin (* x (PI))) (* (pow x 2) (PI)))) (* 1/6 (* (pow tau 2) (* (PI) (sin (* x (PI)))))))))>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))>
#<alt (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI)))))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (/ (sin (* x (PI))) (* (pow tau 2) (* x (PI))))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (/ (sin (* x (PI))) (* (pow tau 2) (* x (PI))))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (/ (sin (* x (PI))) (* (pow tau 2) (* x (PI))))))>
#<alt (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI)))))))>
#<alt (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (/ (sin (* x (PI))) (* (pow tau 2) (* x (PI))))))>
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#<alt (- (cos (* x (* (PI) (- tau 1)))) (cos (* x (* (PI) (+ 1 tau)))))>
#<alt (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))>
#<alt (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))>
#<alt (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))>
#<alt (- (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau)))))) (cos (* x (* (PI) (- 1 (* -1 tau))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* (pow x 2) (* (pow (PI) 2) (pow (- tau 1) 2)))))>
#<alt (+ 1 (* (pow x 2) (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* 1/24 (* (pow x 2) (* (pow (PI) 4) (pow (- tau 1) 4)))))))>
#<alt (+ 1 (* (pow x 2) (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (* (pow (PI) 6) (pow (- tau 1) 6)))) (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))))))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* -1 (* x (PI))))>
#<alt (+ (cos (* -1 (* x (PI)))) (* -1 (* tau (* x (* (PI) (sin (* -1 (* x (PI)))))))))>
#<alt (+ (cos (* -1 (* x (PI)))) (* tau (- (* -1/2 (* tau (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI)))))))) (* x (* (PI) (sin (* -1 (* x (PI)))))))))>
#<alt (+ (cos (* -1 (* x (PI)))) (* tau (- (* tau (+ (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* 1/6 (* tau (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI)))))))))) (* x (* (PI) (sin (* -1 (* x (PI)))))))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* x (* (PI) (- tau 1))))>
#<alt (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))>
#<alt (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))>
#<alt (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))>
#<alt (cos (* -1 (* x (* (PI) (+ 1 (* -1 tau))))))>
#<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 (/ 1 tau)>
#<alt (+ (* 1/6 (* tau (* (pow x 2) (pow (PI) 2)))) (/ 1 tau))>
#<alt (+ (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/36 (* (pow tau 3) (pow (PI) 4))) (* 1/120 (* (pow tau 3) (pow (PI) 4)))))) (* -1/6 (* tau (pow (PI) 2))))) (/ 1 tau))>
#<alt (+ (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/5040 (* (pow tau 5) (pow (PI) 6))) (+ (* 1/720 (* (pow tau 5) (pow (PI) 6))) (* 1/6 (* (pow tau 2) (* (pow (PI) 2) (+ (* -1/36 (* (pow tau 3) (pow (PI) 4))) (* 1/120 (* (pow tau 3) (pow (PI) 4))))))))))) (+ (* -1/36 (* (pow tau 3) (pow (PI) 4))) (* 1/120 (* (pow tau 3) (pow (PI) 4)))))) (* -1/6 (* tau (pow (PI) 2))))) (/ 1 tau))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ 1 tau)>
#<alt (/ (+ 1 (* 1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))) tau)>
#<alt (/ (+ 1 (* (pow tau 2) (- (* -1 (* (pow tau 2) (+ (* -1/36 (* (pow x 4) (pow (PI) 4))) (* 1/120 (* (pow x 4) (pow (PI) 4)))))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))) tau)>
#<alt (/ (+ 1 (* (pow tau 2) (- (* (pow tau 2) (- (* -1 (* (pow tau 2) (+ (* -1/5040 (* (pow x 6) (pow (PI) 6))) (+ (* 1/720 (* (pow x 6) (pow (PI) 6))) (* 1/6 (* (pow x 2) (* (pow (PI) 2) (+ (* -1/36 (* (pow x 4) (pow (PI) 4))) (* 1/120 (* (pow x 4) (pow (PI) 4))))))))))) (+ (* -1/36 (* (pow x 4) (pow (PI) 4))) (* 1/120 (* (pow x 4) (pow (PI) 4)))))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))) tau)>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (/ (* x (PI)) (sin (* tau (* x (PI)))))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<alt (* -1/6 (pow tau 2))>
#<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 (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>
#<alt (* tau (* x (pow (PI) 2)))>

Calls

117 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	(/ (* x (PI)) (sin (* (* x (PI)) tau)))
1.0ms	x	@	inf	(/ (+ (/ 1 x) (* (* -1/6 (* tau tau)) (* x (* (PI) (PI))))) (/ (PI) (sin (* x (PI)))))
1.0ms	tau	@	inf	(+ 1 (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))))
1.0ms	x	@	-inf	(/ (sin (* x (PI))) (/ (* x (PI)) (sin (* (* x (PI)) tau))))
1.0ms	tau	@	0	(/ (+ (/ 1 x) (* (* -1/6 (* tau tau)) (* x (* (PI) (PI))))) (/ (PI) (sin (* x (PI)))))

rewrite340.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3766×	`-lowering-.f32`
3766×	`-lowering-.f64`
2414×	`fma-lowering-fma.f32`
2414×	`fma-lowering-fma.f64`
1902×	`prod-diff`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	258
1	288	249
2	2616	240
0	8167	240

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 660

Calls

Call 1

Inputs
(/ (/ (sin (* x (PI))) (/ (* x (PI)) (sin (* (* x (PI)) tau)))) (* (* x (PI)) tau))
(/ (sin (* x (PI))) (/ (* x (PI)) (sin (* (* x (PI)) tau))))
(sin (* x (PI)))
(* x (PI))
(+ 1 (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))))
(* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)))
(* x x)
(* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))
(/ (+ (/ 1 x) (* (* -1/6 (* tau tau)) (* x (* (PI) (PI))))) (/ (PI) (sin (* x (PI)))))
(+ (/ 1 x) (* (* -1/6 (* tau tau)) (* x (* (PI) (PI)))))
(/ 1 x)
(* (* -1/6 (* tau tau)) (* x (* (PI) (PI))))
(/ (/ (sin (* x (PI))) (PI)) (* (/ (* x (PI)) (sin (* (* x (PI)) tau))) (* x tau)))
(/ (sin (* x (PI))) (PI))
(/ (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* (+ tau 1) x) (PI)))) (* x (* (PI) (* (PI) (* x tau))))) 2)
(/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (* (+ tau 1) x) (PI)))) (* x (* (PI) (* (PI) (* x tau)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (* (+ tau 1) x) (PI))))
(cos (* x (* (PI) (- tau 1))))
(sin (* (* x (PI)) tau))
(/ (* x (PI)) (sin (* (* x (PI)) tau)))
(* (PI) (PI))
(* -1/6 (* tau tau))
(* (PI) (* x tau))
(* (PI) (* (PI) (* x tau)))

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

simplify448.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

5004×	`-lowering-.f32`
5004×	`-lowering-.f64`
3794×	`+-lowering-+.f64`
3794×	`+-lowering-+.f32`
2082×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	646	8264
1	2294	7029
2	6548	6854
0	8693	6854

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 468

Calls

Call 1

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

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

eval138.0ms (1.1%)

Compiler: Compiled 38795 to 2732 computations (93% saved)

prune285.0ms (2.2%)

Pruning

63 alts after pruning (56 fresh and 7 done)

	Pruned	Kept	Total
New	1374	28	1402
Fresh	12	28	40
Picked	2	3	5
Done	1	4	5
Total	1389	63	1452

Accuracy

99.9%

Counts

1452 → 63

Alt Table

Click to see full alt table

Status	Accuracy	Program
	67.1%	(/.f32 (fma.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))) (neg.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))))) #s(literal 2 binary32))
	66.8%	(/.f32 (/.f32 (/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 (PI.f32) (.f32 x (+.f32 tau #s(literal 1 binary32)))))) x) (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) #s(literal 2 binary32))
	96.9%	(/.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (.f32 x tau)) (PI.f32)) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
▶	97.2%	(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))) tau)
	66.9%	(/.f32 (/.f32 (-.f32 (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))))) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))))) (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))))) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	53.1%	(/.f32 (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32)))))) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	53.1%	(/.f32 (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32)))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	66.8%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau))))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
✓	66.8%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	33.3%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	33.3%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	82.5%	(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) x) (/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32)))))
	97.2%	(/.f32 (/.f32 (.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 x (PI.f32))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))) tau) x)
	65.2%	(/.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau)))) (.f32 tau (*.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
	87.2%	(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (*.f32 x (PI.f32)) tau))
	87.4%	(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	86.9%	(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (PI.f32)) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (*.f32 x tau)))
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 x (sin.f32 (.f32 x (PI.f32)))))
	87.2%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))
	72.8%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (.f32 x (PI.f32))))
✓	97.5%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
▶	81.0%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (*.f32 x (PI.f32)) tau))
	97.4%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (/.f32 tau (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
✓	97.9%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
	97.3%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (PI.f32))))
✓	97.3%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)))
	80.9%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) tau) (.f32 (.f32 #s(literal 1/6 binary32) tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) (.f32 x tau)))
	72.9%	(/.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	74.6%	(/.f32 (-.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau)))) #s(literal 2 binary32))
	81.7%	(/.f32 (-.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (.f32 x x) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))))))) #s(literal 1 binary32)) (-.f32 (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau))))) #s(literal 1 binary32)))
	82.2%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))
	71.9%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (.f32 x (PI.f32))))
✓	82.4%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
	87.1%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) tau) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (/.f32 (.f32 (PI.f32) (PI.f32)) tau)))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	96.8%	(/.f32 (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	96.8%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
	81.3%	(/.f32 (.f32 x (+.f32 (.f32 tau (PI.f32)) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (+.f32 tau (.f32 tau (.f32 tau tau)))))))) (.f32 (.f32 x (PI.f32)) tau))
	87.1%	(/.f32 (.f32 x (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)))
	81.5%	(/.f32 (.f32 tau (.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
	71.6%	(/.f32 (.f32 tau (.f32 (.f32 x (PI.f32)) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
✓	81.7%	(/.f32 (.f32 tau (.f32 (sin.f32 (.f32 x (PI.f32))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	96.3%	(/.f32 (.f32 #s(literal -2 binary32) (/.f32 (.f32 (sin.f32 (/.f32 (.f32 x (-.f32 (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32))) (sin.f32 (/.f32 (.f32 x (+.f32 (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32)))) #s(literal 2 binary32))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
▶	97.8%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
▶	66.2%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
	97.0%	(/.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (.f32 (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x tau))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))) (neg.f32 (PI.f32))))
	72.8%	(/.f32 x (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (*.f32 x tau)))
	82.4%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 x x) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (PI.f32) (PI.f32))))
	87.1%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (+.f32 #s(literal 1/120 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32)))))))))
	82.4%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (+.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau tau)))))))
	72.0%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) (PI.f32)))))
▶	66.3%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))
	72.0%	(+.f32 #s(literal 1 binary32) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))))
	97.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) x) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) tau)))
	82.4%	(.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))))) (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))
	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (*.f32 x (pow.f32 (PI.f32) #s(literal 1/3 binary32)))))))
	87.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))))))
	72.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (*.f32 x (PI.f32)) tau)) #s(literal 1 binary32))
	82.4%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau)))))))
	66.8%	(.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (/.f32 #s(literal 1/2 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))))
	81.6%	(.f32 (.f32 tau tau) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 tau tau)))))))
	4.4%	(.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32)))))
✓	65.4%	#s(literal 1 binary32)

Compiler

Compiled 3433 to 1942 computations (43.4% saved)

simplify292.0ms (2.3%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sin.f32 (*.f32 x (PI.f32)))
✓	cost-diff	0	(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
✓	cost-diff	0	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
✓	cost-diff	0	(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))) tau)
✓	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 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))))) tau))
✓	cost-diff	128	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (*.f32 x (PI.f32)) tau))
✓	cost-diff	0	(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 (PI.f32)))
✓	cost-diff	0	(*.f32 x x)
✓	cost-diff	0	(.f32 #s(literal -1/6 binary32) (.f32 x x))
✓	cost-diff	0	(.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))
✓	cost-diff	0	(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 (.f32 (.f32 x (PI.f32)) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))

Rules

4428×	`/-lowering-/.f32`
4428×	`/-lowering-/.f64`
3990×	`associate-/r*`
3610×	`-lowering-.f32`
3610×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	314
1	93	284
2	316	277
3	1185	275
4	2276	275
5	3792	275
6	4294	275
7	4611	275
8	4667	275
9	4675	275
10	4675	275
11	5062	275
12	5172	275
13	5811	275
14	6555	275
15	6875	275
16	6875	275
17	6875	275
0	8798	275

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (sin (* x (PI))) (/ (* (* x (PI)) (* x (* (PI) tau))) (sin (* x (* (PI) tau)))))
(sin (* x (PI)))
(* x (PI))
x
(PI)
(/ (* (* x (PI)) (* x (* (PI) tau))) (sin (* x (* (PI) tau))))
(* (* x (PI)) (* x (* (PI) tau)))
(* x (* (PI) tau))
(* (PI) tau)
tau
(sin (* x (* (PI) tau)))
(+ 1 (* (* -1/6 (* x x)) (* (PI) (PI))))
1
(* (* -1/6 (* x x)) (* (PI) (PI)))
(* -1/6 (* x x))
-1/6
(* x x)
x
(* (PI) (PI))
(PI)
(/ (sin (* x (PI))) (* x (PI)))
(sin (* x (PI)))
(* x (PI))
x
(PI)
(/ (/ (sin (* x (PI))) (/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau)) (* (* x (PI)) tau))
(/ (sin (* x (PI))) (/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau))
(sin (* x (PI)))
(* x (PI))
x
(PI)
(/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau)
(+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI)))))
1
(* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))
(* 1/6 (* tau tau))
1/6
(* tau tau)
tau
(* (* x x) (* (PI) (PI)))
(* x x)
(* (PI) (PI))
(* (* x (PI)) tau)
(/ (/ (/ (sin (* x (PI))) (PI)) (/ (* (* x (PI)) x) (sin (* x (* (PI) tau))))) tau)
(/ (/ (sin (* x (PI))) (PI)) (/ (* (* x (PI)) x) (sin (* x (* (PI) tau)))))
(/ (sin (* x (PI))) (PI))
(sin (* x (PI)))
(* x (PI))
x
(PI)
(/ (* (* x (PI)) x) (sin (* x (* (PI) tau))))
(* (* x (PI)) x)
(sin (* x (* (PI) tau)))
(* x (* (PI) tau))
(* (PI) tau)
tau

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

localize224.0ms (1.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.0%	(*.f32 (PI.f32) tau)
✓	accuracy	98.9%	(/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))
✓	accuracy	98.9%	(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
✓	accuracy	98.7%	(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
✓	accuracy	98.8%	(.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32)))
✓	accuracy	98.6%	(.f32 #s(literal 1/6 binary32) (.f32 tau tau))
✓	accuracy	98.6%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (*.f32 x (PI.f32)) tau))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.2%	(sin.f32 (*.f32 x (PI.f32)))
✓	accuracy	99.0%	(*.f32 x (PI.f32))
✓	accuracy	98.7%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	accuracy	99.8%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))
✓	accuracy	98.8%	(.f32 #s(literal -1/6 binary32) (.f32 x x))
✓	accuracy	98.8%	(.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	98.9%	(/.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))
✓	accuracy	98.9%	(.f32 (.f32 x (PI.f32)) (.f32 x (.f32 (PI.f32) tau)))
✓	accuracy	98.7%	(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
✓	accuracy	98.7%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))

Results

163.0ms

256×

valid

Compiler

Compiled 345 to 35 computations (89.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-mult: 31.0ms (45.9% of total)

ival-div: 15.0ms (22.2% of total)

...c/correct-round.rkt:119:19: 8.0ms (11.8% of total)

ival-sin: 8.0ms (11.8% of total)

ival-add: 3.0ms (4.4% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series47.0ms (0.4%)

Counts

22 → 348

Calls

Call 1

Inputs
#<alt (/ (sin (* x (PI))) (/ (* (* x (PI)) (* x (* (PI) tau))) (sin (* x (* (PI) tau)))))>
#<alt (sin (* x (PI)))>
#<alt (* x (PI))>
#<alt (PI)>
#<alt (+ 1 (* (* -1/6 (* x x)) (* (PI) (PI))))>
#<alt (* (* -1/6 (* x x)) (* (PI) (PI)))>
#<alt (* -1/6 (* x x))>
#<alt (* x x)>
#<alt (/ (sin (* x (PI))) (* x (PI)))>
#<alt (/ (/ (sin (* x (PI))) (/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau)) (* (* x (PI)) tau))>
#<alt (/ (sin (* x (PI))) (/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau))>
#<alt (/ (/ (/ (sin (* x (PI))) (PI)) (/ (* (* x (PI)) x) (sin (* x (* (PI) tau))))) tau)>
#<alt (/ (/ (sin (* x (PI))) (PI)) (/ (* (* x (PI)) x) (sin (* x (* (PI) tau)))))>
#<alt (/ (sin (* x (PI))) (PI))>
#<alt (sin (* x (* (PI) tau)))>
#<alt (* (* x (PI)) (* x (* (PI) tau)))>
#<alt (/ (* (* x (PI)) (* x (* (PI) tau))) (sin (* x (* (PI) tau))))>
#<alt (* (PI) (PI))>
#<alt (* 1/6 (* tau tau))>
#<alt (* (* x x) (* (PI) (PI)))>
#<alt (/ (* (* x (PI)) x) (sin (* x (* (PI) tau))))>
#<alt (* (PI) tau)>

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

Calls

87 calls:

Time	Variable		Point	Expression
14.0ms	tau	@	0	(/ (sin (* x (PI))) (/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau))
3.0ms	x	@	inf	(/ (sin (* x (PI))) (/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau))
3.0ms	x	@	inf	(/ (/ (sin (* x (PI))) (/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau)) (* (* x (PI)) tau))
1.0ms	x	@	inf	(/ (/ (sin (* x (PI))) (PI)) (/ (* (* x (PI)) x) (sin (* x (* (PI) tau)))))
1.0ms	tau	@	inf	(/ (/ (sin (* x (PI))) (/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau)) (* (* x (PI)) tau))

rewrite382.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

3918×	`-lowering-.f32`
3918×	`-lowering-.f64`
3270×	`/-lowering-/.f32`
3270×	`/-lowering-/.f64`
1810×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	206
1	202	182
2	1676	178
0	8547	178

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 642

Calls

Call 1

Inputs
(/ (sin (* x (PI))) (/ (* (* x (PI)) (* x (* (PI) tau))) (sin (* x (* (PI) tau)))))
(sin (* x (PI)))
(* x (PI))
(PI)
(+ 1 (* (* -1/6 (* x x)) (* (PI) (PI))))
(* (* -1/6 (* x x)) (* (PI) (PI)))
(* -1/6 (* x x))
(* x x)
(/ (sin (* x (PI))) (* x (PI)))
(/ (/ (sin (* x (PI))) (/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau)) (* (* x (PI)) tau))
(/ (sin (* x (PI))) (/ (+ 1 (* (* 1/6 (* tau tau)) (* (* x x) (* (PI) (PI))))) tau))
(/ (/ (/ (sin (* x (PI))) (PI)) (/ (* (* x (PI)) x) (sin (* x (* (PI) tau))))) tau)
(/ (/ (sin (* x (PI))) (PI)) (/ (* (* x (PI)) x) (sin (* x (* (PI) tau)))))
(/ (sin (* x (PI))) (PI))
(sin (* x (* (PI) tau)))
(* (* x (PI)) (* x (* (PI) tau)))
(/ (* (* x (PI)) (* x (* (PI) tau))) (sin (* x (* (PI) tau))))
(* (PI) (PI))
(* 1/6 (* tau tau))
(* (* x x) (* (PI) (PI)))
(/ (* (* x (PI)) x) (sin (* x (* (PI) tau))))
(* (PI) tau)

Outputs
(neg.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))))
(exp.f32 (.f32 (log.f32 (/.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (.f32 x (PI.f32))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (*.f32 x (PI.f32)))) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (*.f32 x (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (*.f32 x (PI.f32)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (*.f32 x (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x)))))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (*.f32 x (PI.f32))))))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))))
(/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (neg.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))
(/.f32 (neg.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (neg.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))))
(/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))))) (neg.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
(.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))))
(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))))
(.f32 #s(literal 1 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau))))
(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (neg.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))))))
(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) (pow.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (PI.f32)))) #s(literal -1 binary32)))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) x) (pow.f32 (/.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (.f32 x (PI.f32)))) #s(literal -1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))
(.f32 #s(literal -1 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))))
(.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (neg.f32 (/.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (.f32 x (PI.f32)))))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) (pow.f32 (/.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (.f32 x (PI.f32)))) #s(literal -1 binary32)))
(.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x))))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))))) (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (pow.f32 (/.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (.f32 x (PI.f32)))) #s(literal -1/2 binary32)) (pow.f32 (/.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (*.f32 x (PI.f32)))) #s(literal -1/2 binary32)))
(neg.f32 (neg.f32 (sin.f32 (*.f32 x (PI.f32)))))
(sin.f32 (*.f32 x (PI.f32)))
(-.f32 #s(literal 0 binary32) (neg.f32 (sin.f32 (*.f32 x (PI.f32)))))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sin.f32 (*.f32 x (PI.f32)))))
(/.f32 (neg.f32 (sin.f32 (*.f32 x (PI.f32)))) #s(literal -1 binary32))
(.f32 (sin.f32 (.f32 x (PI.f32))) #s(literal 1 binary32))
(.f32 #s(literal -1 binary32) (neg.f32 (sin.f32 (.f32 x (PI.f32)))))
(neg.f32 (-.f32 #s(literal 0 binary32) (*.f32 x (PI.f32))))
(-.f32 #s(literal 0 binary32) (-.f32 #s(literal 0 binary32) (*.f32 x (PI.f32))))
(/.f32 (*.f32 x (PI.f32)) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) x))
(/.f32 (-.f32 #s(literal 0 binary32) (*.f32 x (PI.f32))) #s(literal -1 binary32))
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(.f32 (.f32 x (PI.f32)) #s(literal 1 binary32))
(.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) x))
(.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) x))
(.f32 #s(literal -1 binary32) (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))))
(.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(PI.f32)
(log1p.f32 (expm1.f32 (PI.f32)))
(neg.f32 (neg.f32 (PI.f32)))
(exp.f32 (log.f32 (PI.f32)))
(exp.f32 (.f32 (.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32))) #s(literal 3 binary32)))
(exp.f32 (.f32 (log.f32 (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1/3 binary32)))
(exp.f32 (.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (PI.f32))) #s(literal 2 binary32)))
(+.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal -1 binary32))
(fabs.f32 (PI.f32))
(pow.f32 (PI.f32) #s(literal 1 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3 binary32))
(pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 1/3 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (E.f32) (log.f32 (PI.f32)))
(-.f32 #s(literal 0 binary32) (neg.f32 (PI.f32)))
(-.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32))
(-.f32 (/.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32)) #s(literal 1 binary32))
(/.f32 (PI.f32) #s(literal 1 binary32))
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(.f32 (sin.f32 (.f32 x (*.f32 (PI.f32) tau))) #s(literal 1 binary32))
(.f32 #s(literal -1 binary32) (neg.f32 (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(neg.f32 (neg.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))))
(-.f32 #s(literal 0 binary32) (neg.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))))
(.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau))))
(.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))
(.f32 (.f32 x (PI.f32)) (.f32 x (.f32 (PI.f32) tau)))
(.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))
(.f32 (.f32 (PI.f32) tau) (.f32 (PI.f32) (.f32 x x)))
(.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x)))) #s(literal 1 binary32))
(.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) tau)
(.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))
(.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (PI.f32) tau))
(.f32 (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau))) x)
(.f32 #s(literal -1 binary32) (neg.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x))))))
(.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) x) (PI.f32))
(.f32 (.f32 (.f32 (PI.f32) (.f32 x x)) tau) (PI.f32))
(neg.f32 (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))
(exp.f32 (.f32 (log.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x)))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) #s(literal 1 binary32))
(pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))
(/.f32 (.f32 x (PI.f32)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau))))
(/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))
(/.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))))))
(/.f32 (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) #s(literal -1 binary32))
(/.f32 (neg.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))))))
(.f32 x (/.f32 (PI.f32) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 x (/.f32 (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (PI.f32) (/.f32 x (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (.f32 x (PI.f32)) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 1 binary32))
(.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (.f32 x (.f32 (PI.f32) tau)) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (.f32 (PI.f32) (.f32 x x)) (/.f32 (.f32 (PI.f32) tau) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (neg.f32 (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) (/.f32 #s(literal -1 binary32) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x)))))
(.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (pow.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x))))) #s(literal -1 binary32)))
(.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (PI.f32)))
(.f32 #s(literal -1 binary32) (.f32 (-.f32 #s(literal 0 binary32) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
(.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (pow.f32 (/.f32 #s(literal -1 binary32) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) #s(literal -1 binary32)) (/.f32 #s(literal -1 binary32) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) #s(literal -1/2 binary32)) (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x))))) #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 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #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 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 4 binary32))
(pow.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))) #s(literal 1/3 binary32))
(sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))))
(cbrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))
(*.f32 (PI.f32) (PI.f32))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32)))
(.f32 (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (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 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 1 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(.f32 (.f32 (PI.f32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32)) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(.f32 (pow.f32 (.f32 (PI.f32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 tau (.f32 tau #s(literal 1/6 binary32)))
(.f32 #s(literal 1 binary32) (.f32 tau (*.f32 tau #s(literal 1/6 binary32))))
(.f32 #s(literal 1/6 binary32) (.f32 tau tau))
(.f32 (.f32 tau tau) #s(literal 1/6 binary32))
(.f32 (.f32 tau #s(literal 1/6 binary32)) tau)
(exp.f32 (.f32 (log.f32 (.f32 x (PI.f32))) #s(literal 2 binary32)))
(exp.f32 (+.f32 (.f32 (log.f32 x) #s(literal 2 binary32)) (.f32 (log.f32 (PI.f32)) #s(literal 2 binary32))))
(exp.f32 (+.f32 (.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (.f32 (PI.f32) (PI.f32)))))
(exp.f32 (+.f32 (.f32 (log.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (log.f32 x) #s(literal 2 binary32))))
(exp.f32 (+.f32 (log.f32 (.f32 (PI.f32) (PI.f32))) (.f32 (log.f32 x) #s(literal 2 binary32))))
(pow.f32 (*.f32 x (PI.f32)) #s(literal 2 binary32))
(.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32))))
(.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x)))
(.f32 (.f32 x (PI.f32)) (*.f32 x (PI.f32)))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))
(.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32)))
(.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 x x))
(.f32 (.f32 (PI.f32) (*.f32 x x)) (PI.f32))
(.f32 (.f32 x (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32)) (pow.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) x) #s(literal 2 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) x) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) x)))
(.f32 (.f32 (.f32 (PI.f32) (.f32 x x)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 (.f32 (.f32 (PI.f32) (.f32 x x)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(.f32 (pow.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(.f32 (pow.f32 (.f32 x (PI.f32)) #s(literal 1 binary32)) (pow.f32 (*.f32 x (PI.f32)) #s(literal 1 binary32)))
(.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 x (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (*.f32 x (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
(neg.f32 (/.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 x x))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(exp.f32 (.f32 (log.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (*.f32 x x)))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) #s(literal 1 binary32))
(pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x x))) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 x x))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 x x))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (.f32 x (PI.f32)) (/.f32 (sin.f32 (.f32 x (*.f32 (PI.f32) tau))) x))
(/.f32 #s(literal 1 binary32) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x x))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x x))))))
(/.f32 (.f32 (PI.f32) (.f32 x x)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))
(/.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) #s(literal 1 binary32))
(/.f32 (/.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 x x))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) #s(literal -1 binary32))
(/.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 x x))) (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x x)))))
(.f32 x (/.f32 (PI.f32) (/.f32 (sin.f32 (.f32 x (*.f32 (PI.f32) tau))) x)))
(.f32 x (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (PI.f32) (/.f32 x (/.f32 (sin.f32 (.f32 x (*.f32 (PI.f32) tau))) x)))
(.f32 (.f32 x (PI.f32)) (/.f32 x (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 x x)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (.f32 (PI.f32) (.f32 x x)) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 1 binary32))
(.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 x x))) (/.f32 #s(literal -1 binary32) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (PI.f32) (*.f32 x x)))
(.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (pow.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 x x))) #s(literal -1 binary32)))
(.f32 (/.f32 x (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (PI.f32)))
(.f32 #s(literal -1 binary32) (/.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 x x))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x x))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (pow.f32 (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 x x))) #s(literal -1 binary32)) (/.f32 #s(literal -1 binary32) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x x))) #s(literal -1/2 binary32)) (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (*.f32 x x))) #s(literal -1/2 binary32)))
(*.f32 (PI.f32) tau)
(*.f32 tau (PI.f32))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) tau))
(.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) tau))
(.f32 (.f32 tau (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 (.f32 tau (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))

simplify507.0ms (4%)

Algorithm

1×	egg-herbie

Rules

8384×	`-lowering-.f32`
8384×	`-lowering-.f64`
3028×	`+-lowering-+.f64`
3028×	`+-lowering-+.f32`
1790×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	597	6228
1	2090	5472
0	8378	5472

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

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

Outputs
1
#s(literal 1 binary32)
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) #s(literal -1/6 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))))))))))
(+.f32 #s(literal 1 binary32) (.f32 x (.f32 x (+.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) #s(literal -1/6 binary32))) (.f32 (.f32 x x) (+.f32 (.f32 (pow.f32 tau #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (*.f32 tau tau))))))))))
(+ 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))))))))))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) #s(literal -1/6 binary32))) (.f32 (.f32 x x) (+.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (+.f32 (.f32 (.f32 x x) (+.f32 (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (+.f32 (.f32 #s(literal -1/720 binary32) (.f32 tau tau)) (.f32 #s(literal -1/720 binary32) (pow.f32 tau #s(literal 4 binary32))))) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (+.f32 (.f32 #s(literal -1/5040 binary32) (pow.f32 tau #s(literal 6 binary32))) #s(literal -1/5040 binary32))))) (.f32 (pow.f32 tau #s(literal 4 binary32)) (*.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 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))))
(+.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))))
(+ (* (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))))
(+.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 tau tau) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 (.f32 x (.f32 x x)) (.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal 1/120 binary32) (.f32 tau tau))))))
(+ (* (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))))
(+.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 tau tau) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 tau tau) (+.f32 (.f32 (.f32 (.f32 #s(literal -1/5040 binary32) (.f32 tau tau)) (pow.f32 x #s(literal 5 binary32))) (.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (PI.f32) #s(literal 5 binary32)))) (.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 x (.f32 x x)) #s(literal 1/120 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)))))
(* x (PI))
(*.f32 x (PI.f32))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(.f32 x (+.f32 (PI.f32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(.f32 x (+.f32 (PI.f32) (.f32 (.f32 x x) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) (.f32 #s(literal 1/120 binary32) (*.f32 x x)))))))
(* 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))))))))
(.f32 x (+.f32 (PI.f32) (.f32 (.f32 x x) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 7 binary32)) #s(literal -1/5040 binary32))) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 5 binary32)))))))))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(* 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))
1
#s(literal 1 binary32)
(+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))
(+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))
(+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))
(* -1/6 (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))
(* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (/ 1 (pow x 2))))
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(/.f32 (+.f32 (/.f32 (.f32 #s(literal -36 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 tau tau) (.f32 (pow.f32 x #s(literal 5 binary32)) (pow.f32 (PI.f32) #s(literal 5 binary32))))) (.f32 (/.f32 #s(literal 6 binary32) (.f32 x (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 tau tau))
(/ (- (+ (* 6 (/ (sin (* x (PI))) (* (pow x 3) (pow (PI) 3)))) (* 216 (/ (sin (* x (PI))) (* (pow tau 4) (* (pow x 7) (pow (PI) 7)))))) (* 36 (/ (sin (* x (PI))) (* (pow tau 2) (* (pow x 5) (pow (PI) 5)))))) (pow tau 2))
(/.f32 (+.f32 (+.f32 (.f32 (/.f32 #s(literal 6 binary32) (.f32 x (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (/.f32 (.f32 #s(literal 216 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (pow.f32 tau #s(literal 4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 7 binary32)) (pow.f32 x #s(literal 7 binary32)))))) (/.f32 (.f32 #s(literal -36 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 tau tau) (.f32 (pow.f32 x #s(literal 5 binary32)) (pow.f32 (PI.f32) #s(literal 5 binary32)))))) (.f32 tau tau))
(/ (- (+ (* -1296 (/ (sin (* x (PI))) (* (pow tau 6) (* (pow x 9) (pow (PI) 9))))) (* 6 (/ (sin (* x (PI))) (* (pow x 3) (pow (PI) 3))))) (+ (* -216 (/ (sin (* x (PI))) (* (pow tau 4) (* (pow x 7) (pow (PI) 7))))) (* 36 (/ (sin (* x (PI))) (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))) (pow tau 2))
(/.f32 (+.f32 (/.f32 (.f32 #s(literal -1296 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (pow.f32 tau #s(literal 6 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 9 binary32)) (pow.f32 x #s(literal 9 binary32))))) (-.f32 (-.f32 (.f32 (/.f32 #s(literal 6 binary32) (.f32 x (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (/.f32 (.f32 #s(literal 36 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 tau tau) (.f32 (pow.f32 x #s(literal 5 binary32)) (pow.f32 (PI.f32) #s(literal 5 binary32)))))) (/.f32 (.f32 #s(literal -216 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (pow.f32 tau #s(literal 4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 7 binary32)) (pow.f32 x #s(literal 7 binary32))))))) (.f32 tau tau))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* x (+ (* tau (PI)) (* (pow x 2) (- (* -1/6 (* tau (pow (PI) 3))) (* 1/6 (* (pow tau 3) (pow (PI) 3)))))))
(.f32 x (+.f32 (.f32 tau (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (+.f32 (.f32 #s(literal -1/6 binary32) tau) (.f32 #s(literal -1/6 binary32) (.f32 tau (*.f32 tau tau))))))))
(* x (+ (* tau (PI)) (* (pow x 2) (- (+ (* -1/6 (* tau (pow (PI) 3))) (* (pow x 2) (- (* 1/120 (* tau (pow (PI) 5))) (* 1/6 (* (pow tau 2) (* (pow (PI) 2) (- (* -1/6 (* tau (pow (PI) 3))) (* 1/6 (* (pow tau 3) (pow (PI) 3)))))))))) (* 1/6 (* (pow tau 3) (pow (PI) 3)))))))
(.f32 x (+.f32 (.f32 tau (PI.f32)) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 x x) (+.f32 (.f32 #s(literal 1/120 binary32) (.f32 tau (pow.f32 (PI.f32) #s(literal 5 binary32)))) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (+.f32 (.f32 #s(literal -1/6 binary32) tau) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))))))))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (+.f32 (.f32 #s(literal -1/6 binary32) tau) (.f32 #s(literal -1/6 binary32) (.f32 tau (*.f32 tau tau)))))))))
(* x (+ (* tau (PI)) (* (pow x 2) (- (+ (* -1/6 (* tau (pow (PI) 3))) (* (pow x 2) (- (+ (* 1/120 (* tau (pow (PI) 5))) (* (pow x 2) (- (* -1/5040 (* tau (pow (PI) 7))) (* 1/6 (* (pow tau 2) (* (pow (PI) 2) (- (* 1/120 (* tau (pow (PI) 5))) (* 1/6 (* (pow tau 2) (* (pow (PI) 2) (- (* -1/6 (* tau (pow (PI) 3))) (* 1/6 (* (pow tau 3) (pow (PI) 3)))))))))))))) (* 1/6 (* (pow tau 2) (* (pow (PI) 2) (- (* -1/6 (* tau (pow (PI) 3))) (* 1/6 (* (pow tau 3) (pow (PI) 3)))))))))) (* 1/6 (* (pow tau 3) (pow (PI) 3)))))))
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(* 6 (/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 #s(literal 6 binary32) (.f32 tau (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) (PI.f32))))
(/ (+ (* -36 (/ (sin (* x (PI))) (* (pow tau 3) (* (pow x 2) (pow (PI) 4))))) (* 6 (/ (sin (* x (PI))) (* tau (pow (PI) 2))))) (pow x 2))
(/.f32 (+.f32 (/.f32 (.f32 #s(literal -36 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 tau (.f32 tau (pow.f32 (PI.f32) #s(literal 4 binary32))))))) (.f32 #s(literal 6 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (PI.f32)))))) (.f32 x x))
(/ (- (+ (* 6 (/ (sin (* x (PI))) (* tau (pow (PI) 2)))) (* 216 (/ (sin (* x (PI))) (* (pow tau 5) (* (pow x 4) (pow (PI) 6)))))) (* 36 (/ (sin (* x (PI))) (* (pow tau 3) (* (pow x 2) (pow (PI) 4)))))) (pow x 2))
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(/ (- (+ (* -1296 (/ (sin (* x (PI))) (* (pow tau 7) (* (pow x 6) (pow (PI) 8))))) (* 6 (/ (sin (* x (PI))) (* tau (pow (PI) 2))))) (+ (* -216 (/ (sin (* x (PI))) (* (pow tau 5) (* (pow x 4) (pow (PI) 6))))) (* 36 (/ (sin (* x (PI))) (* (pow tau 3) (* (pow x 2) (pow (PI) 4))))))) (pow x 2))
(/.f32 (+.f32 (.f32 #s(literal 6 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (PI.f32))))) (-.f32 (/.f32 (.f32 #s(literal -1296 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (pow.f32 x #s(literal 6 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 8 binary32)) (pow.f32 tau #s(literal 7 binary32))))) (+.f32 (/.f32 (.f32 #s(literal 36 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 tau (.f32 tau (pow.f32 (PI.f32) #s(literal 4 binary32))))))) (/.f32 (.f32 #s(literal -216 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (pow.f32 tau #s(literal 5 binary32)) (pow.f32 x #s(literal 4 binary32))) (pow.f32 (PI.f32) #s(literal 6 binary32))))))) (.f32 x x))
(* 6 (/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 #s(literal 6 binary32) (.f32 tau (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) (PI.f32))))
(/ (+ (* -36 (/ (sin (* x (PI))) (* (pow tau 3) (* (pow x 2) (pow (PI) 4))))) (* 6 (/ (sin (* x (PI))) (* tau (pow (PI) 2))))) (pow x 2))
(/.f32 (+.f32 (/.f32 (.f32 #s(literal -36 binary32) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 tau (.f32 tau (pow.f32 (PI.f32) #s(literal 4 binary32))))))) (.f32 #s(literal 6 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (PI.f32)))))) (.f32 x x))
(/ (- (+ (* 6 (/ (sin (* x (PI))) (* tau (pow (PI) 2)))) (* 216 (/ (sin (* x (PI))) (* (pow tau 5) (* (pow x 4) (pow (PI) 6)))))) (* 36 (/ (sin (* x (PI))) (* (pow tau 3) (* (pow x 2) (pow (PI) 4)))))) (pow x 2))
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(/ (- (+ (* -1296 (/ (sin (* x (PI))) (* (pow tau 7) (* (pow x 6) (pow (PI) 8))))) (* 6 (/ (sin (* x (PI))) (* tau (pow (PI) 2))))) (+ (* -216 (/ (sin (* x (PI))) (* (pow tau 5) (* (pow x 4) (pow (PI) 6))))) (* 36 (/ (sin (* x (PI))) (* (pow tau 3) (* (pow x 2) (pow (PI) 4))))))) (pow x 2))
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(* tau (sin (* x (PI))))
(.f32 tau (sin.f32 (.f32 x (PI.f32))))
(* tau (+ (sin (* x (PI))) (* -1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))))))
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(* tau (+ (sin (* x (PI))) (* (pow tau 2) (- (* 1/36 (* (pow tau 2) (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI))))))) (* 1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI))))))))))
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(* tau (+ (sin (* x (PI))) (* (pow tau 2) (- (* (pow tau 2) (- (* -1/216 (* (pow tau 2) (* (pow x 6) (* (pow (PI) 6) (sin (* x (PI))))))) (* -1/36 (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI)))))))) (* 1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI))))))))))
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(* 6 (/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 #s(literal 6 binary32) (.f32 tau (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) (PI.f32))))
(/ (+ (* -36 (/ (sin (* x (PI))) (* (pow tau 2) (* (pow x 4) (pow (PI) 4))))) (* 6 (/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2))))) tau)
(/.f32 (+.f32 (.f32 (/.f32 #s(literal -36 binary32) (.f32 tau (.f32 tau (pow.f32 x #s(literal 4 binary32))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 (/.f32 #s(literal 6 binary32) (.f32 (PI.f32) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x x)))) tau)
(/ (- (+ (* 6 (/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))) (* 216 (/ (sin (* x (PI))) (* (pow tau 4) (* (pow x 6) (pow (PI) 6)))))) (* 36 (/ (sin (* x (PI))) (* (pow tau 2) (* (pow x 4) (pow (PI) 4)))))) tau)
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(/ (- (+ (* -1296 (/ (sin (* x (PI))) (* (pow tau 6) (* (pow x 8) (pow (PI) 8))))) (* 6 (/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2))))) (+ (* -216 (/ (sin (* x (PI))) (* (pow tau 4) (* (pow x 6) (pow (PI) 6))))) (* 36 (/ (sin (* x (PI))) (* (pow tau 2) (* (pow x 4) (pow (PI) 4))))))) tau)
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(* 6 (/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 #s(literal 6 binary32) (.f32 tau (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) (PI.f32))))
(* -1 (/ (+ (* -6 (/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))) (* 36 (/ (sin (* x (PI))) (* (pow tau 2) (* (pow x 4) (pow (PI) 4)))))) tau))
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(* -1 (/ (+ (* -216 (/ (sin (* x (PI))) (* (pow tau 4) (* (pow x 6) (pow (PI) 6))))) (+ (* -6 (/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))) (* 36 (/ (sin (* x (PI))) (* (pow tau 2) (* (pow x 4) (pow (PI) 4))))))) tau))
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(* -1 (/ (+ (* -216 (/ (sin (* x (PI))) (* (pow tau 4) (* (pow x 6) (pow (PI) 6))))) (+ (* -6 (/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))) (+ (* 36 (/ (sin (* x (PI))) (* (pow tau 2) (* (pow x 4) (pow (PI) 4))))) (* 1296 (/ (sin (* x (PI))) (* (pow tau 6) (* (pow x 8) (pow (PI) 8)))))))) tau))
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1
#s(literal 1 binary32)
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(/.f32 (.f32 x (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 tau (PI.f32)))))
(/ (* (pow x 2) (PI)) (sin (* tau (* x (PI)))))
(/.f32 (.f32 x (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 tau (PI.f32)))))
(/ (* (pow x 2) (PI)) (sin (* tau (* x (PI)))))
(/.f32 (.f32 x (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 tau (PI.f32)))))
(/ (* (pow x 2) (PI)) (sin (* tau (* x (PI)))))
(/.f32 (.f32 x (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 tau (PI.f32)))))
(/ (* (pow x 2) (PI)) (sin (* tau (* x (PI)))))
(/.f32 (.f32 x (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 tau (PI.f32)))))
(/ (* (pow x 2) (PI)) (sin (* tau (* x (PI)))))
(/.f32 (.f32 x (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 tau (PI.f32)))))
(/ (* (pow x 2) (PI)) (sin (* tau (* x (PI)))))
(/.f32 (.f32 x (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 tau (PI.f32)))))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))
(* tau (PI))
(*.f32 tau (PI.f32))

eval245.0ms (1.9%)

Compiler: Compiled 55488 to 5657 computations (89.8% saved)

prune389.0ms (3.1%)

Pruning

77 alts after pruning (67 fresh and 10 done)

	Pruned	Kept	Total
New	2149	23	2172
Fresh	7	44	51
Picked	2	3	5
Done	0	7	7
Total	2158	77	2235

Accuracy

99.9%

Counts

2235 → 77

Alt Table

Click to see full alt table

Status	Accuracy	Program
	67.1%	(/.f32 (fma.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))) (neg.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))))) #s(literal 2 binary32))
	66.8%	(/.f32 (/.f32 (/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 (PI.f32) (.f32 x (+.f32 tau #s(literal 1 binary32)))))) x) (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) #s(literal 2 binary32))
	96.5%	(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (.f32 (.f32 (PI.f32) (log.f32 (E.f32))) tau))))) tau)
✓	97.2%	(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))) tau)
	80.8%	(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 x (+.f32 (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (*.f32 tau #s(literal 1/6 binary32))) (/.f32 #s(literal 1 binary32) tau)))) tau)
	66.9%	(/.f32 (/.f32 (-.f32 (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))))) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))))) (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))))) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	53.1%	(/.f32 (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32)))))) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	53.1%	(/.f32 (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32)))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	66.8%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau))))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
✓	66.8%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	33.3%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	33.3%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
	82.5%	(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) x) (/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32)))))
	97.2%	(/.f32 (/.f32 (.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 x (PI.f32))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))) tau) x)
	80.9%	(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 x x) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 x x))))))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (*.f32 x (PI.f32)) tau))
	87.2%	(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (*.f32 x (PI.f32)) tau))
	86.9%	(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (PI.f32)) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (*.f32 x tau)))
	81.3%	(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau))
	86.9%	(/.f32 (/.f32 (.f32 x (+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))) tau)
	70.9%	(/.f32 (/.f32 (.f32 x (PI.f32)) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (*.f32 x (PI.f32)) tau))
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 x (sin.f32 (.f32 x (PI.f32)))))
	87.2%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))
✓	97.5%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
	97.4%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (/.f32 tau (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
✓	97.9%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
	97.3%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (PI.f32))))
✓	97.3%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)))
	72.6%	(/.f32 (/.f32 x (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) tau)
	72.9%	(/.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	74.6%	(/.f32 (-.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau)))) #s(literal 2 binary32))
	81.7%	(/.f32 (-.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (.f32 x x) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))))))) #s(literal 1 binary32)) (-.f32 (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau))))) #s(literal 1 binary32)))
	82.2%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))
	71.9%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (.f32 x (PI.f32))))
✓	82.4%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
	87.1%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) tau) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (/.f32 (.f32 (PI.f32) (PI.f32)) tau)))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	66.3%	(/.f32 (+.f32 (.f32 #s(literal 1/36 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) #s(literal -1 binary32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) #s(literal -1 binary32)))
	81.9%	(/.f32 (+.f32 tau (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (*.f32 tau tau)))))) tau)
	16.3%	(/.f32 (.f32 (/.f32 #s(literal 6 binary32) (.f32 tau (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (PI.f32)))) (.f32 (*.f32 x (PI.f32)) tau))
	96.8%	(/.f32 (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	96.8%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
	81.3%	(/.f32 (.f32 x (+.f32 (.f32 tau (PI.f32)) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (+.f32 tau (.f32 tau (.f32 tau tau)))))))) (.f32 (.f32 x (PI.f32)) tau))
	87.2%	(/.f32 (.f32 x (+.f32 (PI.f32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))) (/.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
	87.1%	(/.f32 (.f32 x (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)))
	65.2%	(/.f32 (.f32 x (.f32 tau (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
	81.5%	(/.f32 (.f32 tau (.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
	71.6%	(/.f32 (.f32 tau (.f32 (.f32 x (PI.f32)) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
✓	81.7%	(/.f32 (.f32 tau (.f32 (sin.f32 (.f32 x (PI.f32))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	96.3%	(/.f32 (.f32 #s(literal -2 binary32) (/.f32 (.f32 (sin.f32 (/.f32 (.f32 x (-.f32 (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32))) (sin.f32 (/.f32 (.f32 x (+.f32 (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32)))) #s(literal 2 binary32))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	97.8%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (*.f32 x (PI.f32))))
	97.2%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 x x)) (/.f32 (.f32 (PI.f32) tau) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
	81.3%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 (PI.f32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) (*.f32 x x)))))
✓	66.2%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
	72.8%	(/.f32 x (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (*.f32 x tau)))
	96.7%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x)))))))
	66.2%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))
	66.3%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))))))
	66.3%	(+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) #s(literal 1 binary32))
	66.3%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x #s(literal -1/6 binary32))) x))
	82.4%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 x x) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (PI.f32) (PI.f32))))
	87.1%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (+.f32 #s(literal 1/120 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32)))))))))
	82.4%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (+.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau tau)))))))
	72.0%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) (PI.f32)))))
	66.3%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32)) (PI.f32))))
✓	66.3%	(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))
	72.0%	(+.f32 #s(literal 1 binary32) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))))
	97.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) x) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) tau)))
	82.4%	(.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))))) (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))
	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (*.f32 x (pow.f32 (PI.f32) #s(literal 1/3 binary32)))))))
	87.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))))))
	72.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (*.f32 x (PI.f32)) tau)) #s(literal 1 binary32))
	80.8%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (/.f32 (/.f32 tau (+.f32 #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal 1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x))))))) x))
	82.4%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau)))))))
	66.8%	(.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (/.f32 #s(literal 1/2 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))))
	4.7%	(.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))
	81.6%	(.f32 (.f32 tau tau) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 tau tau)))))))
✓	65.4%	#s(literal 1 binary32)

Compiler

Compiled 5250 to 1795 computations (65.8% saved)

regimes168.0ms (1.3%)

Counts

119 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x #s(literal -1/6 binary32))) x))
(+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) #s(literal 1 binary32))
(/.f32 (.f32 x (.f32 tau (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
(.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32)))))
(+.f32 #s(literal 1 binary32) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32)) (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) #s(literal -1/6 binary32)))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 x x) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (PI.f32) (PI.f32))))
(/.f32 (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (+.f32 tau (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (*.f32 tau tau)))))) tau)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (.f32 x (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (+.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau tau)))))))
(.f32 (.f32 tau tau) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 tau tau)))))))
(/.f32 (/.f32 (.f32 x (PI.f32)) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (*.f32 x (PI.f32)) tau))
(/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau))))) (.f32 tau (*.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
(/.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau)))) (.f32 tau (*.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
(/.f32 (.f32 x (+.f32 (.f32 tau (PI.f32)) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (+.f32 tau (.f32 tau (.f32 tau tau)))))))) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (+.f32 (.f32 #s(literal 1/36 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) #s(literal -1 binary32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) #s(literal -1 binary32)))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))
(/.f32 (.f32 tau (.f32 (.f32 x (PI.f32)) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (/.f32 (.f32 (.f32 x x) (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau)))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))) #s(literal 2 binary32))
(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (.f32 tau (.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (.f32 x x) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))))))) #s(literal 1 binary32)) (-.f32 (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau))))) #s(literal 1 binary32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (*.f32 x (PI.f32)) tau)) #s(literal 1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(/.f32 x (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (*.f32 x tau)))
(/.f32 (/.f32 x (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) tau)
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau)))))))
(.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))))) (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 6 binary32) (.f32 tau (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (PI.f32)))) (.f32 (*.f32 x (PI.f32)) tau))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
(.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 (PI.f32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) (*.f32 x x)))))
(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) x) (/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32)))))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) tau) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (/.f32 (.f32 (PI.f32) (PI.f32)) tau)))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) tau) (.f32 (.f32 #s(literal 1/6 binary32) tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) (.f32 x tau)))
(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 x (+.f32 (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (*.f32 tau #s(literal 1/6 binary32))) (/.f32 #s(literal 1 binary32) tau)))) tau)
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (/.f32 (/.f32 tau (+.f32 #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal 1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x))))))) x))
(/.f32 (.f32 x (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (*.f32 x (PI.f32)) tau))
(/.f32 (/.f32 (.f32 x (+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))) tau)
(/.f32 (.f32 x (+.f32 (PI.f32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))) (/.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))
(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (PI.f32)) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (*.f32 x tau)))
(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (*.f32 x (PI.f32)) tau))
(/.f32 (.f32 tau (.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (/.f32 (.f32 x (+.f32 (.f32 tau (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/.f32 (.f32 tau (.f32 (sin.f32 (.f32 x (PI.f32))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32)))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
(/.f32 (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32)))))) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (+.f32 #s(literal 1/120 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32)))))))))
(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 x x) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 x x))))))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (*.f32 x (PI.f32)) tau))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) x) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) tau)))
(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) tau) (PI.f32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 x x)) (/.f32 (.f32 (PI.f32) tau) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (*.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 x (PI.f32)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (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 (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 x tau)) (PI.f32))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (/.f32 tau (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) tau)) (.f32 (/.f32 (.f32 x (PI.f32)) (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)))) (/.f32 x (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (.f32 x (PI.f32)) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))) tau)
(/.f32 (/.f32 (.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 x (PI.f32))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))) tau) x)
(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))) tau)
(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 x (sin.f32 (.f32 (PI.f32) (.f32 x tau))))) x) (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
(/.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (.f32 x tau)) (PI.f32)) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (.f32 (PI.f32) tau)) x) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (.f32 (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x tau))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))) (neg.f32 (PI.f32))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x)))))))
(/.f32 (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (/.f32 #s(literal 1/2 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))) #s(literal 2 binary32))
(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (-.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) tau))))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
(/.f32 (/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))) (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau)))) x) #s(literal 2 binary32))
(/.f32 (/.f32 (/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 (PI.f32) (.f32 x (+.f32 tau #s(literal 1 binary32)))))) x) (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) #s(literal 2 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (-.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))))) #s(literal 2 binary32))
(/.f32 (-.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau)))) #s(literal 2 binary32))
(-.f32 (/.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (/.f32 (/.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))) #s(literal 2 binary32)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))))
(/.f32 (/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) x) (.f32 x (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))))) (*.f32 x x)) #s(literal 2 binary32))
(/.f32 (.f32 #s(literal -2 binary32) (/.f32 (.f32 (sin.f32 (/.f32 (.f32 x (-.f32 (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32))) (sin.f32 (/.f32 (.f32 x (+.f32 (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) #s(literal 2 binary32)))) #s(literal 2 binary32))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (.f32 (.f32 (PI.f32) (log.f32 (E.f32))) tau))))) tau)
(/.f32 (fma.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))) (neg.f32 (/.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))) (.f32 (.f32 x (PI.f32)) (.f32 (.f32 x (PI.f32)) tau))))) #s(literal 2 binary32))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32)) (.f32 x tau)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 1/3 binary32))) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 1/3 binary32))) tau))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (pow.f32 (/.f32 x (sin.f32 (.f32 x (PI.f32)))) #s(literal -1 binary32)) (pow.f32 (/.f32 (/.f32 (PI.f32) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau))) #s(literal -1 binary32)))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 x (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
(/.f32 (/.f32 (-.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32)))))))) (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))))))) (.f32 #s(literal 2 binary32) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (*.f32 x (pow.f32 (PI.f32) #s(literal 1/3 binary32)))))))
(/.f32 (/.f32 (-.f32 (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32)))))))) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32))))))) (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))))) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal -1 binary32))))) (cos.f32 (.f32 x (.f32 (PI.f32) (+.f32 tau #s(literal 1 binary32)))))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
(/.f32 (-.f32 (pow.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) #s(literal 3 binary32)) (pow.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))) #s(literal 3 binary32))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #s(literal 2 binary32))) (+.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32)))))))) (.f32 (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))) (+.f32 (cos.f32 (.f32 x (.f32 (PI.f32) (-.f32 tau #s(literal 1 binary32))))) (cos.f32 (.f32 (*.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32)))))))))

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

Calls

4 calls:

46.0ms	(*.f32 x (PI.f32))
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))))
33.0ms	tau
32.0ms	x

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes69.0ms (0.5%)

Counts

67 → 1

Calls

Call 1

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

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

Calls

3 calls:

19.0ms	x
18.0ms	tau
18.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
87.8%	1	`x`
87.8%	1	`(*.f32 x (PI.f32))`
87.8%	1	`tau`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes60.0ms (0.5%)

Counts

45 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x #s(literal -1/6 binary32))) x))
(+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) #s(literal 1 binary32))
(/.f32 (.f32 x (.f32 tau (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
(.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32)))))
(+.f32 #s(literal 1 binary32) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32)) (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) #s(literal -1/6 binary32)))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 x x) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (PI.f32) (PI.f32))))
(/.f32 (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (+.f32 tau (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (*.f32 tau tau)))))) tau)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (.f32 x (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (+.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau tau)))))))
(.f32 (.f32 tau tau) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 tau tau)))))))
(/.f32 (/.f32 (.f32 x (PI.f32)) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (*.f32 x (PI.f32)) tau))
(/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau))))) (.f32 tau (*.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
(/.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau)))) (.f32 tau (*.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
(/.f32 (.f32 x (+.f32 (.f32 tau (PI.f32)) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (+.f32 tau (.f32 tau (.f32 tau tau)))))))) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (+.f32 (.f32 #s(literal 1/36 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) #s(literal -1 binary32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) #s(literal -1 binary32)))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))
(/.f32 (.f32 tau (.f32 (.f32 x (PI.f32)) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (/.f32 (.f32 (.f32 x x) (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau)))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))) #s(literal 2 binary32))
(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (.f32 tau (.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (.f32 x x) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))))))) #s(literal 1 binary32)) (-.f32 (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau))))) #s(literal 1 binary32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (*.f32 x (PI.f32)) tau)) #s(literal 1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(/.f32 x (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (*.f32 x tau)))
(/.f32 (/.f32 x (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) tau)
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau)))))))
(.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))))) (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 6 binary32) (.f32 tau (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (PI.f32)))) (.f32 (*.f32 x (PI.f32)) tau))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
(.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

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

Calls

3 calls:

13.0ms	tau
13.0ms	(*.f32 x (PI.f32))
12.0ms	x

Results

Accuracy	Segments	Branch
82.7%	1	`x`
82.7%	1	`(*.f32 x (PI.f32))`
82.7%	1	`tau`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes51.0ms (0.4%)

Counts

44 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x #s(literal -1/6 binary32))) x))
(+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) #s(literal 1 binary32))
(/.f32 (.f32 x (.f32 tau (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
(.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32)))))
(+.f32 #s(literal 1 binary32) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32)) (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) #s(literal -1/6 binary32)))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 x x) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (PI.f32) (PI.f32))))
(/.f32 (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (+.f32 tau (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (*.f32 tau tau)))))) tau)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (.f32 x (PI.f32))))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (+.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau tau)))))))
(.f32 (.f32 tau tau) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (+.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 tau tau)))))))
(/.f32 (/.f32 (.f32 x (PI.f32)) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (*.f32 x (PI.f32)) tau))
(/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau))))) (.f32 tau (*.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
(/.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau)))) (.f32 tau (*.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32))
(/.f32 (.f32 x (+.f32 (.f32 tau (PI.f32)) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (+.f32 tau (.f32 tau (.f32 tau tau)))))))) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (+.f32 (.f32 #s(literal 1/36 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))))) #s(literal -1 binary32)) (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x)))) #s(literal -1 binary32)))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))
(/.f32 (.f32 tau (.f32 (.f32 x (PI.f32)) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (/.f32 (.f32 (.f32 x x) (.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (-.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 tau #s(literal -1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) tau) (+.f32 #s(literal 1 binary32) tau)))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))) #s(literal 2 binary32))
(/.f32 (/.f32 (.f32 x (+.f32 (PI.f32) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (.f32 tau (.f32 (.f32 x (+.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (+.f32 (.f32 x (PI.f32)) (.f32 (.f32 tau (.f32 tau (.f32 x (.f32 x x)))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32)))))) (.f32 x (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (.f32 (.f32 x x) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))))))) #s(literal 1 binary32)) (-.f32 (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 #s(literal -1/6 binary32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau))))) #s(literal 1 binary32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (*.f32 x (PI.f32)) tau)) #s(literal 1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(/.f32 x (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (*.f32 x tau)))
(/.f32 (/.f32 x (/.f32 (.f32 (.f32 x (PI.f32)) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) tau)
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (PI.f32) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau)))))))
(.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))))) (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 6 binary32) (.f32 tau (.f32 x x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (PI.f32)))) (.f32 (*.f32 x (PI.f32)) tau))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 x (PI.f32)) (+.f32 tau #s(literal 1 binary32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (cos.f32 (.f32 (.f32 (+.f32 tau #s(literal 1 binary32)) x) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(literal 2 binary32))

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

Calls

3 calls:

21.0ms	(*.f32 x (PI.f32))
13.0ms	x
12.0ms	tau

Results

Accuracy	Segments	Branch
82.4%	1	`x`
82.4%	1	`tau`
82.4%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes91.0ms (0.7%)

Counts

39 → 1

Calls

Call 1

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

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

Calls

3 calls:

53.0ms	x
25.0ms	(*.f32 x (PI.f32))
10.0ms	tau

Results

Accuracy	Segments	Branch
82.4%	1	`x`
82.4%	1	`(*.f32 x (PI.f32))`
82.4%	1	`tau`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes10.0ms (0.1%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	tau
4.0ms	x

Results

Accuracy	Segments	Branch
82.4%	1	`x`
82.4%	1	`tau`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes16.0ms (0.1%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	tau
4.0ms	x

Results

Accuracy	Segments	Branch
72.0%	1	`x`
72.0%	1	`tau`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts

7 → 1

Calls

Call 1

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

Outputs
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x #s(literal -1/6 binary32))) x))

Calls

2 calls:

3.0ms	tau
3.0ms	x

Results

Accuracy	Segments	Branch
66.3%	1	`x`
66.3%	1	`tau`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs

#s(literal 1 binary32)

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

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

Outputs
(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32))))

Calls

2 calls:

10.0ms	x
2.0ms	tau

Results

Accuracy	Segments	Branch
66.3%	1	`x`
66.3%	1	`tau`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -19.8b remaining (-179%)

Threshold costs -19.8b (-179%)

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(literal 1 binary32)

Calls

2 calls:

1.0ms	x
1.0ms	tau

Results

Accuracy	Segments	Branch
65.4%	1	`x`
65.4%	1	`tau`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

52×	`*-commutative_binary32`
18×	`+-commutative_binary32`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	163
1	87	163

Stop Event

1×

saturated

Calls

Call 1

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

soundness2.2s (17.3%)

Rules

5240×	`-lowering-.f32`
5240×	`-lowering-.f64`
5212×	`-lowering-.f32`
5212×	`-lowering-.f64`
5200×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	646	8264
1	2294	7029
2	6548	6854
0	8693	6854
0	17	105
1	101	105
2	778	98
3	7573	98
0	8437	98
0	626	7880
1	2262	6993
2	6359	6883
0	8499	6883
0	45	258
1	288	249
2	2616	240
0	8167	240
0	265	3255
1	931	2974
2	4084	2860
0	8093	2860
0	34	206
1	202	182
2	1676	178
0	8547	178

Stop Event

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

Compiler

Compiled 402 to 217 computations (46% saved)

preprocess66.0ms (0.5%)

Remove

(abs tau)

(abs x)

Compiler

Compiled 1112 to 438 computations (60.6% saved)

analyze33.0ms (0.3%)

sample2.1s (16.2%)

preprocess84.0ms (0.7%)

explain131.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify38.0ms (0.3%)

localize139.0ms (1.1%)

series34.0ms (0.3%)

rewrite362.0ms (2.8%)

simplify285.0ms (2.2%)

eval127.0ms (1%)

prune268.0ms (2.1%)

simplify486.0ms (3.8%)

localize302.0ms (2.4%)

series100.0ms (0.8%)

rewrite548.0ms (4.3%)

simplify480.0ms (3.8%)

eval185.0ms (1.4%)

prune272.0ms (2.1%)

simplify337.0ms (2.6%)

localize373.0ms (2.9%)

series37.0ms (0.3%)

rewrite340.0ms (2.7%)

simplify448.0ms (3.5%)

eval138.0ms (1.1%)

prune285.0ms (2.2%)

simplify292.0ms (2.3%)

localize224.0ms (1.8%)

series47.0ms (0.4%)

rewrite382.0ms (3%)

simplify507.0ms (4%)

eval245.0ms (1.9%)

prune389.0ms (3.1%)

regimes168.0ms (1.3%)

regimes69.0ms (0.5%)

regimes60.0ms (0.5%)

regimes51.0ms (0.4%)

regimes91.0ms (0.7%)

regimes10.0ms (0.1%)

regimes16.0ms (0.1%)

regimes6.0ms (0%)

regimes13.0ms (0.1%)

regimes3.0ms (0%)

simplify9.0ms (0.1%)

soundness2.2s (17.3%)

preprocess66.0ms (0.5%)

end0.0ms (0%)

Profiling