Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample2.4s (46.2%)

Results

2.4s

8256×

body

128

valid

preprocess80.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

967×	`associate-/l/_binary32`
808×	`associate-/l*_binary32`
710×	`times-frac_binary32`
520×	`associate-/r/_binary32`
385×	`associate-*r/_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	72
1	49	72
2	173	72
3	733	72
4	2487	72
5	3267	72
6	3267	72
7	4554	72
8	4807	72
9	4927	72
10	4939	72
11	4939	72
12	4941	72
13	4941	72
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

745×	`associate-/l/_binary32`
396×	`associate-/l*_binary32`
281×	`times-frac_binary32`
253×	`associate-/r/_binary32`
154×	`associate-*l/_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	24	36
2	83	36
3	333	36
4	1180	36
5	2559	36
6	2687	36
7	2717	36
8	2727	36
9	2731	36
10	2733	36
11	2733	36

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.8b	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (.f32 x (*.f32 x (PI.f32)))))
▶	0.6b	(.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

Error

Program

0.8b

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

▶

0.6b

(*.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 136 to 64 computations (52.9% saved)

localize38.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f32 x (PI.f32))
✓	0.3b	(.f32 (.f32 x (PI.f32)) tau)
✓	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

series19.0ms (0.4%)

Counts

4 → 68

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	tau	@	inf	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
2.0ms	x	@	inf	(.f32 (.f32 x (PI.f32)) tau)
2.0ms	x	@	0	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
1.0ms	x	@	-inf	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
1.0ms	tau	@	-inf	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

rewrite65.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

720×	`prod-diff_binary32`
203×	`expm1-udef_binary32`
203×	`log1p-udef_binary32`
111×	`*-un-lft-identity_binary32`
111×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	47
1	213	47
2	3114	47

Stop Event

1×	node limit

Counts

4 → 113

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (/.f32 (/.f32 1 x) (PI.f32)) tau))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) (cbrt.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 2)) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (/.f32 (/.f32 1 x) (PI.f32)) tau)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (/.f32 (/.f32 1 x) (PI.f32)) tau)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 1 (.f32 (.f32 x (PI.f32)) (neg.f32 tau))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (/.f32 1 x) (PI.f32)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (/.f32 (/.f32 1 x) (PI.f32)) tau) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32))) (/.f32 1 tau))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 x) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) tau)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (PI.f32) tau)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) x) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (PI.f32) tau)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (.f32 x (PI.f32))) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) tau))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (PI.f32))) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) tau))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) tau) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 tau) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) tau) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) 1) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 1) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (cbrt.f32 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (cbrt.f32 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 x (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) tau))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (.f32 x (PI.f32)) (neg.f32 tau))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) 3) (pow.f32 (.f32 x (.f32 (PI.f32) tau)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (/.f32 1 x) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (/.f32 1 x) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) 2) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (/.f32 1 x) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 1 (.f32 (PI.f32) (neg.f32 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (/.f32 1 x) (PI.f32)) (sin.f32 (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (/.f32 1 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) 1) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) 1) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) x) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 x) (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (PI.f32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 2)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (sqrt.f32 (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (PI.f32)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) (PI.f32)) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 2)) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 2)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) (sqrt.f32 (.f32 x (PI.f32)))) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (sqrt.f32 (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (neg.f32 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3) (pow.f32 (.f32 x (PI.f32)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 x (.f32 (PI.f32) tau)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 x (.f32 (PI.f32) tau)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 x (.f32 (PI.f32) tau)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 x (.f32 (PI.f32) tau)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 tau) (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 x (.f32 (PI.f32) tau)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (.f32 x (PI.f32)) 3) (pow.f32 tau 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 tau 3) (pow.f32 (.f32 x (PI.f32)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 x (.f32 (PI.f32) tau))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 x (.f32 (PI.f32) tau))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 x (PI.f32)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 x (PI.f32)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 x (PI.f32)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 x (PI.f32)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 x (PI.f32))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 x (PI.f32))))))))

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

588×	`associate-/r*_binary32`
515×	`associate-+l+_binary32`
395×	`associate-l_binary32`
379×	`associate-r_binary32`
321×	`associate-/l/_binary32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	55	982
1	148	974
2	433	964
3	2160	964
4	2821	964
5	3929	937

Stop Event

1×	node limit

Counts

181 → 135

Calls

Call 1

Inputs
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2))))
(+.f32 (.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4))) (+.f32 1 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2)))))
(+.f32 (.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2))) (.f32 -1/5040 (.f32 (pow.f32 x 6) (pow.f32 (PI.f32) 6))))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)

Outputs
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(+.f32 1 (.f32 -1/6 (.f32 (.f32 (.f32 tau tau) (pow.f32 (PI.f32) 2)) (*.f32 x x))))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) 1)
(fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) 1)
(fma.f32 (.f32 tau tau) (.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) 1)
(+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 1 (fma.f32 -1/6 (.f32 (.f32 (.f32 tau tau) (pow.f32 (PI.f32) 2)) (.f32 x x)) (.f32 1/120 (.f32 (*.f32 (pow.f32 tau 4) (pow.f32 (PI.f32) 4)) (pow.f32 x 4)))))
(+.f32 1 (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (*.f32 1/120 (pow.f32 tau 4)))))
(fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1))
(fma.f32 (.f32 tau tau) (.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) (fma.f32 (.f32 (pow.f32 (PI.f32) 4) (.f32 1/120 (pow.f32 tau 4))) (pow.f32 x 4) 1))
(fma.f32 -1/6 (.f32 tau (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)))) (fma.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (.f32 tau (PI.f32)) 4)) 1))
(+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (+.f32 1 (fma.f32 -1/6 (.f32 (.f32 (.f32 tau tau) (pow.f32 (PI.f32) 2)) (.f32 x x)) (.f32 1/120 (.f32 (*.f32 (pow.f32 tau 4) (pow.f32 (PI.f32) 4)) (pow.f32 x 4))))))
(+.f32 (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (.f32 1/120 (pow.f32 tau 4)))) (fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (*.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) 1))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1)))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (fma.f32 (.f32 tau tau) (.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) (fma.f32 (.f32 (pow.f32 (PI.f32) 4) (.f32 1/120 (pow.f32 tau 4))) (pow.f32 x 4) 1)))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (pow.f32 (.f32 (PI.f32) x) 6)) (fma.f32 -1/6 (.f32 tau (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)))) (fma.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (.f32 tau (PI.f32)) 4)) 1)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(+.f32 1 (.f32 -1/6 (.f32 (.f32 (.f32 tau tau) (pow.f32 (PI.f32) 2)) (*.f32 x x))))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) 1)
(fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) 1)
(fma.f32 (.f32 tau tau) (.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) 1)
(+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 1 (fma.f32 -1/6 (.f32 (.f32 (.f32 tau tau) (pow.f32 (PI.f32) 2)) (.f32 x x)) (.f32 1/120 (.f32 (*.f32 (pow.f32 tau 4) (pow.f32 (PI.f32) 4)) (pow.f32 x 4)))))
(+.f32 1 (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (*.f32 1/120 (pow.f32 tau 4)))))
(fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1))
(fma.f32 (.f32 tau tau) (.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) (fma.f32 (.f32 (pow.f32 (PI.f32) 4) (.f32 1/120 (pow.f32 tau 4))) (pow.f32 x 4) 1))
(fma.f32 -1/6 (.f32 tau (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)))) (fma.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (.f32 tau (PI.f32)) 4)) 1))
(+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (+.f32 1 (fma.f32 -1/6 (.f32 (.f32 (.f32 tau tau) (pow.f32 (PI.f32) 2)) (.f32 x x)) (.f32 1/120 (.f32 (*.f32 (pow.f32 tau 4) (pow.f32 (PI.f32) 4)) (pow.f32 x 4))))))
(+.f32 (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (.f32 1/120 (pow.f32 tau 4)))) (fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (*.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) 1))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1)))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (fma.f32 (.f32 tau tau) (.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) (fma.f32 (.f32 (pow.f32 (PI.f32) 4) (.f32 1/120 (pow.f32 tau 4))) (pow.f32 x 4) 1)))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (pow.f32 (.f32 (PI.f32) x) 6)) (fma.f32 -1/6 (.f32 tau (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)))) (fma.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (.f32 tau (PI.f32)) 4)) 1)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (*.f32 x x))))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) 1)
(+.f32 (.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4))) (+.f32 1 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2)))))
(fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (+.f32 1 (.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)))))
(fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (*.f32 x x)) 1))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) (fma.f32 (pow.f32 x 4) (*.f32 1/120 (pow.f32 (PI.f32) 4)) 1))
(fma.f32 (pow.f32 x 4) (.f32 1/120 (pow.f32 (PI.f32) 4)) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (*.f32 x x)) 1))
(fma.f32 1/120 (pow.f32 (.f32 (PI.f32) x) 4) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (*.f32 x x)) 1))
(+.f32 (.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2))) (.f32 -1/5040 (.f32 (pow.f32 x 6) (pow.f32 (PI.f32) 6))))))
(fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (+.f32 1 (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) (.f32 -1/5040 (*.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))))))
(fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (+.f32 (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) 1) (.f32 -1/5040 (*.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))))
(fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) (fma.f32 -1/5040 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)) 1)))
(fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 -1/5040 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) 1)))
(fma.f32 1/120 (pow.f32 (.f32 (PI.f32) x) 4) (fma.f32 -1/5040 (pow.f32 (.f32 (PI.f32) x) 6) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) 1)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)

prune518.0ms (10.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	186	14	200
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	187	15	202

Error

0.0b

Counts

202 → 15

Alt Table

Status	Error	Program
	1.1b	(.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	2.9b	(.f32 (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (/.f32 (/.f32 1 x) (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (pow.f32 (sqrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.1b	(.f32 (+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (.f32 x (*.f32 x (PI.f32)))))
	1.2b	(.f32 (/.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 3)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (pow.f32 (/.f32 x (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) tau))) -1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 3) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 6065 to 1629 computations (73.1% saved)

localize43.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f32 x (PI.f32))
✓	0.3b	(.f32 (PI.f32) (.f32 tau x))
	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.4b	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))

series4.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	tau	@	0	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
0.0ms	tau	@	inf	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
0.0ms	x	@	0	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
0.0ms	tau	@	-inf	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
0.0ms	x	@	-inf	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))

rewrite48.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

879×	`log1p-expm1-u_binary32`
879×	`expm1-log1p-u_binary32`
86×	`*-un-lft-identity_binary32`
86×	`add-sqr-sqrt_binary32`
86×	`pow1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	166	28
2	2301	28

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 2) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 1 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 1 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 1 (.f32 (.f32 tau x) (neg.f32 (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 1 (.f32 tau x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) 1) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 1) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (PI.f32)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 tau x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (PI.f32)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 tau x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (PI.f32)) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 tau x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 tau x)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (.f32 tau x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (.f32 tau x)) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (cbrt.f32 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (cbrt.f32 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (.f32 (PI.f32) tau)) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (PI.f32) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (.f32 tau x) (neg.f32 (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) 3) (pow.f32 (.f32 x (.f32 (PI.f32) tau)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 x (.f32 (PI.f32) tau)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 x (.f32 (PI.f32) tau)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 x (.f32 (PI.f32) tau)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 x (.f32 (PI.f32) tau)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (pow.f32 (exp.f32 tau) x) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 x (.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 x (.f32 (PI.f32) tau)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 tau x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (.f32 tau x) 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 x (.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 x (.f32 (PI.f32) tau))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 x (*.f32 (PI.f32) tau))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (/.f32 1 (*.f32 x (*.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))) 2) (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) 2) (*.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (/.f32 1 (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))) (sqrt.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (*.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (/.f32 1 (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (neg.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (/.f32 1 (*.f32 (*.f32 tau x) (neg.f32 (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (*.f32 x (*.f32 (PI.f32) tau))) (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (PI.f32)) (/.f32 1 (*.f32 tau x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) 2) 1) (/.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (*.f32 x (*.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) 1) (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (*.f32 x (*.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (PI.f32)) (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (*.f32 tau x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (PI.f32)) (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 tau x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) 2) (PI.f32)) (/.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (*.f32 tau x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (*.f32 tau x)) (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (*.f32 tau x)) (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) 2) (*.f32 tau x)) (/.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (pow.f32 (cbrt.f32 (*.f32 x (*.f32 (PI.f32) tau))) 2)) (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (cbrt.f32 (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) 2) (pow.f32 (cbrt.f32 (*.f32 x (*.f32 (PI.f32) tau))) 2)) (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (pow.f32 (cbrt.f32 (*.f32 x (*.f32 (PI.f32) tau))) 2)) (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (cbrt.f32 (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (sqrt.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (sqrt.f32 (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) 2) (sqrt.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (/.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (sqrt.f32 (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (*.f32 (PI.f32) tau)) (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) 2) (*.f32 (PI.f32) tau)) (/.f32 (cbrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) (*.f32 (PI.f32) tau)) (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (*.f32 x (*.f32 (PI.f32) tau)) (sin.f32 (*.f32 x (*.f32 (PI.f32) tau)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 (*.f32 tau x) (neg.f32 (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) 3) (pow.f32 (*.f32 x (*.f32 (PI.f32) tau)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (*.f32 x (*.f32 (PI.f32) tau)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 x (*.f32 (PI.f32) tau)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 x (*.f32 (PI.f32) tau)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 x (*.f32 (PI.f32) tau)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 x (*.f32 (PI.f32) tau))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 x (*.f32 (PI.f32) tau))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 x (*.f32 (PI.f32) tau)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (pow.f32 (exp.f32 tau) x) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 x (*.f32 (PI.f32) tau)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 x (*.f32 (PI.f32) tau)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 tau x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (*.f32 tau x) 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 x (*.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 x (*.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 x (*.f32 (PI.f32) tau))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 x (*.f32 (PI.f32) tau))))))))

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

935×	`fma-def_binary32`
481×	`associate-/r*_binary32`
352×	`associate-l_binary32`
340×	`associate-r_binary32`
275×	`associate-/l/_binary32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	42	772
1	106	768
2	323	760
3	1801	760
4	3094	760
5	3946	742

Stop Event

1×	node limit

Counts

106 → 70

Calls

Call 1

Inputs
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))

Outputs
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(+.f32 1 (.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (*.f32 x x)))))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) 1)
(fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) 1)
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 x x) tau) tau)) 1)
(+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 1 (fma.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 1 (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 (pow.f32 tau 4) (.f32 (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1/120))))
(fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) (fma.f32 (pow.f32 tau 4) (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1))
(fma.f32 (pow.f32 x 4) (.f32 1/120 (.f32 (pow.f32 tau 4) (pow.f32 (PI.f32) 4))) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 x x) tau) tau)) 1))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 x x) tau) tau)) (fma.f32 1/120 (.f32 (pow.f32 tau 4) (pow.f32 (.f32 (PI.f32) x) 4)) 1))
(+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (+.f32 1 (fma.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(+.f32 (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 (pow.f32 tau 4) (.f32 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1/120))) (fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (*.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) 1))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) (fma.f32 (pow.f32 tau 4) (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1)))
(fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) (fma.f32 (pow.f32 tau 4) (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) (fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) 1)))
(fma.f32 (pow.f32 (PI.f32) 6) (.f32 -1/5040 (.f32 (pow.f32 tau 6) (pow.f32 x 6))) (fma.f32 (pow.f32 x 4) (.f32 1/120 (.f32 (pow.f32 tau 4) (pow.f32 (PI.f32) 4))) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 x x) tau) tau)) 1)))
(fma.f32 1/120 (.f32 (pow.f32 tau 4) (pow.f32 (.f32 (PI.f32) x) 4)) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 x x) tau) tau)) (fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (pow.f32 (.f32 (PI.f32) x) 6)) 1)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(+.f32 1 (.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (*.f32 x x)))))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) 1)
(fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) 1)
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 x x) tau) tau)) 1)
(+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 1 (fma.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 1 (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 (pow.f32 tau 4) (.f32 (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1/120))))
(fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) (fma.f32 (pow.f32 tau 4) (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1))
(fma.f32 (pow.f32 x 4) (.f32 1/120 (.f32 (pow.f32 tau 4) (pow.f32 (PI.f32) 4))) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 x x) tau) tau)) 1))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 x x) tau) tau)) (fma.f32 1/120 (.f32 (pow.f32 tau 4) (pow.f32 (.f32 (PI.f32) x) 4)) 1))
(+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (+.f32 1 (fma.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(+.f32 (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 (pow.f32 tau 4) (.f32 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1/120))) (fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (*.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) 1))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) (fma.f32 (pow.f32 tau 4) (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1)))
(fma.f32 -1/6 (.f32 tau (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) tau))) (fma.f32 (pow.f32 tau 4) (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) (fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) 1)))
(fma.f32 (pow.f32 (PI.f32) 6) (.f32 -1/5040 (.f32 (pow.f32 tau 6) (pow.f32 x 6))) (fma.f32 (pow.f32 x 4) (.f32 1/120 (.f32 (pow.f32 tau 4) (pow.f32 (PI.f32) 4))) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 x x) tau) tau)) 1)))
(fma.f32 1/120 (.f32 (pow.f32 tau 4) (pow.f32 (.f32 (PI.f32) x) 4)) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 x x) tau) tau)) (fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (pow.f32 (.f32 (PI.f32) x) 6)) 1)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))

prune285.0ms (5.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	167	15	182

Error

0.0b

Counts

182 → 15

Alt Table

Status	Error	Program
	1.1b	(.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	2.9b	(.f32 (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (/.f32 (/.f32 1 x) (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.1b	(.f32 (+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 3)))
	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (pow.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32)))) -1))
	0.8b	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (.f32 x (*.f32 x (PI.f32)))))
	1.2b	(.f32 (/.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 3)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 1 (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))

Compiler

Compiled 5278 to 1433 computations (72.8% saved)

localize44.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))
	0.3b	(.f32 (.f32 x (PI.f32)) tau)
✓	0.4b	(/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32)))
	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32)))
0.0ms	x	@	inf	(/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32)))
0.0ms	x	@	-inf	(/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32)))
0.0ms	x	@	0	(expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))
0.0ms	x	@	inf	(expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))

rewrite46.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

807×	`pow1_binary32`
748×	`expm1-log1p-u_binary32`
747×	`log1p-expm1-u_binary32`
73×	`*-un-lft-identity_binary32`
73×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	147	19
2	1956	19

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

Inputs
(/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32)))
(expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sin.f32 (*.f32 x (PI.f32))) (/.f32 (/.f32 1 x) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))) 2) (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) 2) (*.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (/.f32 (/.f32 1 x) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (*.f32 (sqrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (/.f32 (/.f32 1 x) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (neg.f32 (sin.f32 (*.f32 x (PI.f32)))) (/.f32 1 (*.f32 x (neg.f32 (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (/.f32 1 x) (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) x) (/.f32 1 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) 2) 1) (/.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (*.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (PI.f32)))) 1) (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (*.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (PI.f32)))) x) (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) 2) x) (/.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (PI.f32)) (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (PI.f32)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (PI.f32)) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) 2) (PI.f32)) (/.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 2)) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (cbrt.f32 (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) 2) (pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 2)) (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 2)) (/.f32 (sqrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (cbrt.f32 (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (sqrt.f32 (*.f32 x (PI.f32)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (sqrt.f32 (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) 2) (sqrt.f32 (*.f32 x (PI.f32)))) (/.f32 (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))) (sqrt.f32 (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 x (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (neg.f32 (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (sin.f32 (*.f32 x (PI.f32))) 3) (pow.f32 (*.f32 x (PI.f32)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (*.f32 x (PI.f32)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 x (PI.f32)) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 x (PI.f32))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (PI.f32) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 x (PI.f32)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (*.f32 x (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 x) 2) (*.f32 (cbrt.f32 x) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (*.f32 x (PI.f32))) (pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 2) (cbrt.f32 (*.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (*.f32 (cbrt.f32 (PI.f32)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 x) (*.f32 (sqrt.f32 x) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (*.f32 x (PI.f32))) (sqrt.f32 (*.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (PI.f32)) (*.f32 (sqrt.f32 (PI.f32)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 x (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (PI.f32) (pow.f32 (cbrt.f32 x) 2)) (cbrt.f32 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (PI.f32) (sqrt.f32 x)) (sqrt.f32 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (+.f32 (*.f32 x (PI.f32)) 1) 3) 1) (+.f32 (*.f32 (+.f32 (*.f32 x (PI.f32)) 1) (+.f32 (*.f32 x (PI.f32)) 1)) (+.f32 1 (*.f32 (+.f32 (*.f32 x (PI.f32)) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (*.f32 (+.f32 (*.f32 x (PI.f32)) 1) (+.f32 (*.f32 x (PI.f32)) 1)) 1) (+.f32 (+.f32 (*.f32 x (PI.f32)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 x (PI.f32)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 x (PI.f32)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 x (PI.f32))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 x (PI.f32)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 x) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 x (PI.f32)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 x (PI.f32))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 x (PI.f32))))))))

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Rules

989×	`fma-def_binary32`
473×	`associate-/r*_binary32`
360×	`*-commutative_binary32`
295×	`associate-/l/_binary32`
280×	`sqr-pow_binary32`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	33	266
1	79	262
2	206	260
3	856	260
4	2199	254
5	2831	251
6	3713	242
7	4468	242
8	4720	242

Stop Event

1×	node limit

Counts

96 → 81

Calls

Call 1

Inputs
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2))))
(+.f32 (.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4))) (+.f32 1 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2)))))
(+.f32 (.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2))) (.f32 -1/5040 (.f32 (pow.f32 x 6) (pow.f32 (PI.f32) 6))))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)
(*.f32 (PI.f32) x)

Outputs
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2))))
(+.f32 1 (.f32 -1/6 (.f32 (*.f32 x x) (pow.f32 (PI.f32) 2))))
(fma.f32 -1/6 (.f32 (.f32 x x) (pow.f32 (PI.f32) 2)) 1)
(fma.f32 (.f32 x x) (.f32 -1/6 (pow.f32 (PI.f32) 2)) 1)
(fma.f32 -1/6 (pow.f32 (*.f32 x (PI.f32)) 2) 1)
(+.f32 (.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4))) (+.f32 1 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2)))))
(fma.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4)) (+.f32 1 (.f32 -1/6 (.f32 (.f32 x x) (pow.f32 (PI.f32) 2)))))
(fma.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4)) (fma.f32 -1/6 (.f32 (*.f32 x x) (pow.f32 (PI.f32) 2)) 1))
(fma.f32 -1/6 (.f32 x (.f32 x (pow.f32 (PI.f32) 2))) (fma.f32 1/120 (*.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4)) 1))
(fma.f32 -1/6 (.f32 (.f32 x x) (pow.f32 (PI.f32) 2)) (fma.f32 1/120 (*.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4)) 1))
(fma.f32 1/120 (pow.f32 (.f32 x (PI.f32)) 4) (fma.f32 -1/6 (.f32 (*.f32 x x) (pow.f32 (PI.f32) 2)) 1))
(fma.f32 (pow.f32 (.f32 x (PI.f32)) 2) (fma.f32 (pow.f32 (.f32 x (PI.f32)) 2) 1/120 -1/6) 1)
(+.f32 (.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2))) (.f32 -1/5040 (.f32 (pow.f32 x 6) (pow.f32 (PI.f32) 6))))))
(fma.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4)) (+.f32 1 (fma.f32 -1/6 (.f32 (.f32 x x) (pow.f32 (PI.f32) 2)) (.f32 -1/5040 (*.f32 (pow.f32 x 6) (pow.f32 (PI.f32) 6))))))
(+.f32 (fma.f32 -1/6 (.f32 (.f32 x x) (pow.f32 (PI.f32) 2)) (.f32 -1/5040 (.f32 (pow.f32 x 6) (pow.f32 (PI.f32) 6)))) (fma.f32 1/120 (*.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4)) 1))
(fma.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4)) (fma.f32 (.f32 x x) (.f32 -1/6 (pow.f32 (PI.f32) 2)) (fma.f32 (pow.f32 x 6) (.f32 -1/5040 (pow.f32 (PI.f32) 6)) 1)))
(fma.f32 -1/6 (.f32 (.f32 x x) (pow.f32 (PI.f32) 2)) (fma.f32 1/120 (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4)) (fma.f32 -1/5040 (.f32 (pow.f32 x 6) (pow.f32 (PI.f32) 6)) 1)))
(fma.f32 -1/6 (.f32 (.f32 x x) (pow.f32 (PI.f32) 2)) (fma.f32 1/120 (pow.f32 (.f32 x (PI.f32)) 4) (fma.f32 -1/5040 (.f32 (pow.f32 x 6) (pow.f32 (PI.f32) 6)) 1)))
(fma.f32 -1/6 (.f32 (.f32 x x) (pow.f32 (PI.f32) 2)) (fma.f32 1/120 (pow.f32 (.f32 x (PI.f32)) 4) (fma.f32 -1/5040 (pow.f32 (.f32 x (PI.f32)) 6) 1)))
(fma.f32 (pow.f32 (.f32 x (PI.f32)) 2) (fma.f32 (pow.f32 (.f32 x (PI.f32)) 2) 1/120 -1/6) (fma.f32 -1/5040 (pow.f32 (*.f32 x (PI.f32)) 6) 1))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))

prune312.0ms (6.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	169	15	184

Error

0.0b

Counts

184 → 15

Alt Table

Status	Error	Program
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 2) (.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (/.f32 (/.f32 1 x) (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 3)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.1b	(.f32 (+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 3)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 x) 2) (.f32 (cbrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 3)))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (pow.f32 (/.f32 x (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32))) -1))
	2.9b	(.f32 (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (.f32 x (*.f32 x (PI.f32)))))
✓	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
▶	0.7b	(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))

Compiler

Compiled 5518 to 1493 computations (72.9% saved)

localize51.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 x (.f32 (PI.f32) tau))
✓	0.3b	(*.f32 (PI.f32) tau)
	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.4b	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (*.f32 (PI.f32) tau))))

series8.0ms (0.2%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	tau	@	-inf	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (*.f32 (PI.f32) tau))))
1.0ms	tau	@	inf	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (*.f32 (PI.f32) tau))))
1.0ms	tau	@	0	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (*.f32 (PI.f32) tau))))
1.0ms	x	@	0	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (*.f32 (PI.f32) tau))))
0.0ms	tau	@	0	(.f32 x (.f32 (PI.f32) tau))

rewrite51.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

539×	`log-prod_binary32`
493×	`prod-diff_binary32`
175×	`expm1-udef_binary32`
175×	`log1p-udef_binary32`
154×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	202	33
2	2563	33

Stop Event

1×	node limit

Counts

3 → 78

Calls

Call 1

Inputs
(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (*.f32 (PI.f32) tau))))
(*.f32 (PI.f32) tau)
(.f32 x (.f32 (PI.f32) tau))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (*.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32)))))) (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32)))))))) (log.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (*.f32 tau (*.f32 x (PI.f32))) (sin.f32 (*.f32 tau (*.f32 x (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (cbrt.f32 (pow.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) 2)) (/.f32 (*.f32 tau (*.f32 x (PI.f32))) (cbrt.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (sqrt.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32))))) (/.f32 (*.f32 tau (*.f32 x (PI.f32))) (sqrt.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32))))) (neg.f32 (*.f32 tau (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 (PI.f32) tau)) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) x) (*.f32 (PI.f32) tau))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (sqrt.f32 (*.f32 tau (*.f32 x (PI.f32))))) (sqrt.f32 (*.f32 tau (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) 1) (*.f32 tau (*.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (pow.f32 (cbrt.f32 (*.f32 tau (*.f32 x (PI.f32)))) 2)) (cbrt.f32 (*.f32 tau (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 x (PI.f32))) tau)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 -1 (sin.f32 (*.f32 tau (*.f32 x (PI.f32))))) (neg.f32 (*.f32 tau (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (/.f32 1 x) (sin.f32 (*.f32 tau (*.f32 x (PI.f32))))) (*.f32 (PI.f32) tau))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) -1) (neg.f32 (*.f32 tau (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (/.f32 1 x)) (*.f32 (PI.f32) tau))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) 3) (pow.f32 (*.f32 tau (*.f32 x (PI.f32))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) 3) (pow.f32 (/.f32 1 (*.f32 tau (*.f32 x (PI.f32)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (/.f32 1 (*.f32 tau (*.f32 x (PI.f32)))) 3) (pow.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 tau (*.f32 x (PI.f32)))) (*.f32 tau (*.f32 x (PI.f32))))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (PI.f32) tau))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (*.f32 (cbrt.f32 (pow.f32 (exp.f32 (PI.f32)) tau)) (cbrt.f32 (pow.f32 (exp.f32 (PI.f32)) tau)))) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (PI.f32)) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (PI.f32)) tau))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (PI.f32)) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) tau))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (PI.f32) tau) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (PI.f32) tau) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (PI.f32) tau)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (PI.f32) tau)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (PI.f32) tau) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (PI.f32)) tau))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (PI.f32) tau))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (PI.f32) tau) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 tau 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 tau 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (PI.f32) tau)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (PI.f32) tau)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (PI.f32) tau)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (PI.f32) tau)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 tau (*.f32 x (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (*.f32 (cbrt.f32 (pow.f32 (pow.f32 (exp.f32 (PI.f32)) tau) x)) (cbrt.f32 (pow.f32 (pow.f32 (exp.f32 (PI.f32)) tau) x)))) (log.f32 (cbrt.f32 (pow.f32 (pow.f32 (exp.f32 (PI.f32)) tau) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (pow.f32 (exp.f32 (PI.f32)) tau) x))) (log.f32 (sqrt.f32 (pow.f32 (pow.f32 (exp.f32 (PI.f32)) tau) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 tau (*.f32 x (PI.f32))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 x (/.f32 1 (*.f32 (PI.f32) tau)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (PI.f32) tau) (/.f32 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 tau (*.f32 x (PI.f32))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 1 (*.f32 tau (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (pow.f32 (cbrt.f32 (*.f32 tau (*.f32 x (PI.f32)))) 2) (/.f32 1 (cbrt.f32 (*.f32 tau (*.f32 x (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (sqrt.f32 (*.f32 tau (*.f32 x (PI.f32)))) (pow.f32 (*.f32 tau (*.f32 x (PI.f32))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (*.f32 tau (*.f32 x (PI.f32)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 x (PI.f32)) (/.f32 1 tau))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 tau (*.f32 x (PI.f32))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 tau (*.f32 x (PI.f32))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 tau (*.f32 x (PI.f32)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 tau (*.f32 x (PI.f32)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 tau (*.f32 x (PI.f32))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (pow.f32 (exp.f32 (PI.f32)) tau) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 tau (*.f32 x (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 tau (*.f32 x (PI.f32))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 x 3) (pow.f32 (*.f32 (PI.f32) tau) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (*.f32 (PI.f32) tau) 3) (pow.f32 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 tau (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 tau (*.f32 x (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 tau (*.f32 x (PI.f32)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 tau (*.f32 x (PI.f32)))))))))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

995×	`fma-def_binary32`
474×	`associate-/r*_binary32`
425×	`associate-l_binary32`
388×	`associate-r_binary32`
275×	`associate-/l/_binary32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	58	828
1	153	820
2	420	820
3	2168	820
4	3443	820
5	4325	802

Stop Event

1×	node limit

Counts

138 → 96

Calls

Call 1

Inputs
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
1
(+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2)))) 1)
(+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2)))) (+.f32 1 (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4))))))
(+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2)))) (+.f32 1 (+.f32 (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4)))) (.f32 -1/5040 (.f32 (pow.f32 tau 6) (*.f32 (pow.f32 x 6) (pow.f32 (PI.f32) 6)))))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))

Outputs
1
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(fma.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) 1)
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) 1)
(fma.f32 (.f32 tau (.f32 tau (.f32 x x))) (.f32 -1/6 (pow.f32 (PI.f32) 2)) 1)
(fma.f32 (pow.f32 (PI.f32) 2) (.f32 -1/6 (.f32 tau (.f32 tau (.f32 x x)))) 1)
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) 1)
(+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(+.f32 (fma.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) 1) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) (fma.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) (fma.f32 (.f32 (pow.f32 tau 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) (pow.f32 x 4) 1))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) (fma.f32 (pow.f32 x 4) (.f32 (pow.f32 tau 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) 1))
(fma.f32 (pow.f32 tau 4) (.f32 (pow.f32 x 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) 1))
(fma.f32 (pow.f32 (PI.f32) 4) (.f32 1/120 (pow.f32 (.f32 tau x) 4)) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) 1))
(+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))))
(fma.f32 -1/5040 (.f32 (.f32 (pow.f32 tau 6) (pow.f32 x 6)) (pow.f32 (PI.f32) 6)) (+.f32 (fma.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) 1) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) (fma.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1)))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) (fma.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) (fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) 1)))
(fma.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (.f32 -1/5040 (pow.f32 x 6))) (fma.f32 (pow.f32 tau 4) (.f32 (pow.f32 x 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) 1)))
(fma.f32 (pow.f32 x 6) (.f32 -1/5040 (pow.f32 (.f32 tau (PI.f32)) 6)) (fma.f32 (pow.f32 (PI.f32) 4) (.f32 1/120 (pow.f32 (.f32 tau x) 4)) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) 1)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
1
(+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (*.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2)))) 1)
(fma.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) 1)
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) 1)
(fma.f32 (.f32 tau (.f32 tau (.f32 x x))) (.f32 -1/6 (pow.f32 (PI.f32) 2)) 1)
(fma.f32 (pow.f32 (PI.f32) 2) (.f32 -1/6 (.f32 tau (.f32 tau (.f32 x x)))) 1)
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) 1)
(+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2)))) (+.f32 1 (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4))))))
(+.f32 (fma.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) 1) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)))))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) (fma.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) (fma.f32 (.f32 (pow.f32 tau 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) (pow.f32 x 4) 1))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) (fma.f32 (pow.f32 x 4) (.f32 (pow.f32 tau 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) 1))
(fma.f32 (pow.f32 tau 4) (.f32 (pow.f32 x 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) 1))
(fma.f32 (pow.f32 (PI.f32) 4) (.f32 1/120 (pow.f32 (.f32 tau x) 4)) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) 1))
(+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 x 2) (pow.f32 (PI.f32) 2)))) (+.f32 1 (+.f32 (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 x 4) (pow.f32 (PI.f32) 4)))) (.f32 -1/5040 (.f32 (pow.f32 tau 6) (*.f32 (pow.f32 x 6) (pow.f32 (PI.f32) 6)))))))
(fma.f32 -1/5040 (.f32 (.f32 (pow.f32 tau 6) (pow.f32 x 6)) (pow.f32 (PI.f32) 6)) (+.f32 (fma.f32 -1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))) 1) (.f32 1/120 (.f32 (pow.f32 tau 4) (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))
(fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) (fma.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1)))
(fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) (fma.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) (fma.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) 1)))
(fma.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (.f32 -1/5040 (pow.f32 x 6))) (fma.f32 (pow.f32 tau 4) (.f32 (pow.f32 x 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) 1)))
(fma.f32 (pow.f32 x 6) (.f32 -1/5040 (pow.f32 (.f32 tau (PI.f32)) 6)) (fma.f32 (pow.f32 (PI.f32) 4) (.f32 1/120 (pow.f32 (.f32 tau x) 4)) (fma.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 tau (.f32 tau (.f32 x x)))) 1)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(*.f32 tau (PI.f32))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))
(.f32 tau (.f32 (PI.f32) x))
(.f32 (.f32 tau x) (PI.f32))
(.f32 (PI.f32) (.f32 tau x))

prune336.0ms (6.5%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	187	5	192
Fresh	3	10	13
Picked	0	1	1
Done	0	1	1
Total	190	17	207

Error

0.0b

Counts

207 → 17

Alt Table

Status	Error	Program
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 3)))
	1.2b	(.f32 (.f32 (sin.f32 (/.f32 (pow.f32 (cbrt.f32 (.f32 tau (.f32 x (PI.f32)))) 2) (/.f32 1 (cbrt.f32 (.f32 tau (.f32 x (PI.f32))))))) (/.f32 1 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 3)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32)))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.1b	(.f32 (+.f32 (.f32 -1/5040 (.f32 (pow.f32 tau 6) (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))) (+.f32 1 (+.f32 (.f32 -1/6 (.f32 (pow.f32 tau 2) (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))) (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 3)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 x) 2) (.f32 (cbrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (pow.f32 (/.f32 x (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32))) -1))
	0.8b	(.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))))) 3) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 tau (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (.f32 x (*.f32 x (PI.f32)))))
✓	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (.f32 (PI.f32) tau)))) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) 1))
✓	0.7b	(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 1 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))

Compiler

Compiled 5810 to 1761 computations (69.7% saved)

regimes377.0ms (7.3%)

Accuracy

Total -4.1b remaining (-612.1%)

Threshold costs -4.1b (-612.1%)

Counts

129 → 1

Compiler

Compiled 3409 to 806 computations (76.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	16	36

Stop Event

1×

saturated

Calls

Call 1

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

Outputs

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

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

end158.0ms (3.1%)

Stop Event

1×

fuel

Compiler

Compiled 512 to 162 computations (68.4% saved)

Details

analyze1.0ms (0%)

sample2.4s (46.2%)

preprocess80.0ms (1.5%)

simplify37.0ms (0.7%)

prune3.0ms (0.1%)

localize38.0ms (0.7%)

series19.0ms (0.4%)

rewrite65.0ms (1.3%)

simplify67.0ms (1.3%)

prune518.0ms (10.1%)

localize43.0ms (0.8%)

series4.0ms (0.1%)

rewrite48.0ms (0.9%)

simplify54.0ms (1.1%)

prune285.0ms (5.5%)

localize44.0ms (0.9%)

series2.0ms (0%)

rewrite46.0ms (0.9%)

simplify53.0ms (1%)

prune312.0ms (6.1%)

localize51.0ms (1%)

series8.0ms (0.2%)

rewrite51.0ms (1%)

simplify63.0ms (1.2%)

prune336.0ms (6.5%)

regimes377.0ms (7.3%)

simplify2.0ms (0%)

end158.0ms (3.1%)

Profiling