Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample2.0s (38.1%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 76 to 42 computations (44.7% saved)

preprocess79.0ms (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)

simplify38.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.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)))))

Status

Error

Program

▶

0.7b

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

0.9b

(*.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)))))

Compiler

Compiled 136 to 64 computations (52.9% saved)

localize35.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series16.0ms (0.3%)

Counts

4 → 72

Calls

18 calls:

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

rewrite63.0ms (1.2%)

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	49
1	213	49
2	3114	49

Stop Event

1×	node limit

Counts

4 → 116

Calls

Call 1

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

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-neg_binary32`
450×	`distribute-rgt-neg-in_binary32`
440×	`distribute-lft-neg-in_binary32`
299×	`*-commutative_binary32`
299×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	1330
1	245	1314
2	918	1298
3	2787	1298
4	4771	1298

Stop Event

1×	node limit

Counts

188 → 143

Calls

Call 1

Inputs
1
(-.f32 1 (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))))
(-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))))
(-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
1
(-.f32 1 (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (*.f32 (pow.f32 tau 2) (pow.f32 x 2)))))
(-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (pow.f32 tau 2) (pow.f32 x 2)))))
(-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6)))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (*.f32 (pow.f32 tau 2) (pow.f32 x 2))))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
1
(-.f32 1 (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (*.f32 (pow.f32 tau 2) (pow.f32 x 2)))))
(-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (pow.f32 tau 2) (pow.f32 x 2)))))
(-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6)))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (*.f32 (pow.f32 tau 2) (pow.f32 x 2))))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
(.f32 (PI.f32) (.f32 tau x))
(-.f32 (.f32 (PI.f32) (.f32 tau x)) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 tau 3) (pow.f32 x 3)))))
(-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 5) (.f32 (pow.f32 tau 5) (pow.f32 x 5)))) (.f32 (PI.f32) (.f32 tau x))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 tau 3) (pow.f32 x 3)))))
(-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 5) (.f32 (pow.f32 tau 5) (pow.f32 x 5)))) (.f32 (PI.f32) (.f32 tau x))) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 tau 7) (pow.f32 x 7)))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 tau 3) (pow.f32 x 3))))))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(.f32 (PI.f32) (.f32 tau x))
(-.f32 (.f32 (PI.f32) (.f32 tau x)) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 tau 3) (pow.f32 x 3)))))
(-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 5) (.f32 (pow.f32 tau 5) (pow.f32 x 5)))) (.f32 (PI.f32) (.f32 tau x))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 tau 3) (pow.f32 x 3)))))
(-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 5) (.f32 (pow.f32 tau 5) (pow.f32 x 5)))) (.f32 (PI.f32) (.f32 tau x))) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 tau 7) (pow.f32 x 7)))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 tau 3) (pow.f32 x 3))))))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
(sin.f32 (.f32 (PI.f32) (.f32 tau 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)

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

prune221.0ms (4.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	176	15	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	177	16	193

Error

0.1b

Counts

193 → 16

Alt Table

Status	Error	Program
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.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))))))
	2.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 1 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) -1/6) (.f32 (pow.f32 x 6) (.f32 (pow.f32 (PI.f32) 6) -1/5040))))))
	1.0b	(.f32 (.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)) (/.f32 (sin.f32 (.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)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	0.9b	(.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)))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.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))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 2)) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (PI.f32))))
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.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))))
	1.3b	(.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))))
	0.9b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32))) (/.f32 1 tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.6b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (.f32 (/.f32 (/.f32 1 x) (PI.f32)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	5.3b	(.f32 (/.f32 (sin.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 6051 to 1718 computations (71.6% saved)

localize42.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(expm1.f32 (*.f32 x (PI.f32)))
0.0ms	x	@	0	(/.f32 (sin.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32)))
0.0ms	x	@	-inf	(/.f32 (sin.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32)))
0.0ms	x	@	inf	(expm1.f32 (*.f32 x (PI.f32)))
0.0ms	x	@	inf	(/.f32 (sin.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32)))

rewrite42.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

800×	`pow1_binary32`
741×	`expm1-log1p-u_binary32`
740×	`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	21
1	148	21
2	1948	21

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

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

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

simplify30.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

735×	`cancel-sign-sub-inv_binary32`
551×	`unswap-sqr_binary32`
349×	`distribute-rgt-neg-in_binary32`
348×	`associate-r_binary32`
341×	`associate-l_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	366
1	138	366
2	432	359
3	2203	359

Stop Event

1×	node limit

Counts

84 → 77

Calls

Call 1

Inputs
1
(-.f32 1 (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))))
(-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))))
(-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(*.f32 (PI.f32) x)
(+.f32 (.f32 1/2 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))) (*.f32 (PI.f32) x))
(+.f32 (.f32 1/2 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))) (+.f32 (.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3))) (*.f32 (PI.f32) x)))
(+.f32 (.f32 1/2 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))) (+.f32 (.f32 1/24 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) (+.f32 (.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3))) (*.f32 (PI.f32) x))))
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)

Outputs
1
(-.f32 1 (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))))
(+.f32 1 (.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (*.f32 x x))))
(+.f32 1 (.f32 (.f32 x (*.f32 x (pow.f32 (PI.f32) 2))) -1/6))
(fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) -1/6 1)
(-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))))
(+.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1) (.f32 -1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))))
(+.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1) (.f32 (.f32 x (.f32 x (pow.f32 (PI.f32) 2))) -1/6))
(fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) -1/6 (fma.f32 1/120 (*.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1))
(fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (*.f32 x x)) -1/6 1))
(-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2)))))
(-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1) (fma.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (*.f32 x x)))))
(-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1) (fma.f32 1/6 (.f32 x (.f32 x (pow.f32 (PI.f32) 2))) (.f32 1/5040 (*.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)))))
(+.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1) (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) -1/6 (.f32 (*.f32 -1/5040 (pow.f32 x 6)) (pow.f32 (PI.f32) 6))))
(+.f32 1 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 x 6) -1/5040) (.f32 (.f32 (pow.f32 (PI.f32) 2) (*.f32 x x)) -1/6))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(*.f32 (PI.f32) x)
(+.f32 (.f32 1/2 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))) (*.f32 (PI.f32) x))
(fma.f32 1/2 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) (*.f32 (PI.f32) x))
(fma.f32 (PI.f32) x (.f32 (.f32 x (*.f32 x (pow.f32 (PI.f32) 2))) 1/2))
(.f32 x (+.f32 (PI.f32) (.f32 (pow.f32 (PI.f32) 2) (*.f32 1/2 x))))
(.f32 x (+.f32 (.f32 x (*.f32 1/2 (pow.f32 (PI.f32) 2))) (PI.f32)))
(+.f32 (.f32 1/2 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))) (+.f32 (.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3))) (*.f32 (PI.f32) x)))
(fma.f32 1/2 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3)) (.f32 (PI.f32) x)))
(fma.f32 (.f32 x (.f32 x (pow.f32 (PI.f32) 2))) 1/2 (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3)) (.f32 (PI.f32) x)))
(fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3)) (.f32 x (+.f32 (PI.f32) (.f32 (pow.f32 (PI.f32) 2) (.f32 1/2 x)))))
(fma.f32 (PI.f32) x (.f32 (.f32 x x) (+.f32 (.f32 1/2 (pow.f32 (PI.f32) 2)) (.f32 1/6 (*.f32 x (pow.f32 (PI.f32) 3))))))
(+.f32 (.f32 1/2 (.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))) (+.f32 (.f32 1/24 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) (+.f32 (.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3))) (*.f32 (PI.f32) x))))
(fma.f32 1/2 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) (fma.f32 1/24 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3)) (*.f32 (PI.f32) x))))
(fma.f32 (.f32 x (.f32 x (pow.f32 (PI.f32) 2))) 1/2 (fma.f32 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1/24 (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3)) (*.f32 (PI.f32) x))))
(fma.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 x 4) 1/24) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3)) (.f32 x (+.f32 (PI.f32) (.f32 (pow.f32 (PI.f32) 2) (*.f32 1/2 x))))))
(fma.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 x 4) 1/24) (fma.f32 (PI.f32) x (.f32 (.f32 x x) (+.f32 (.f32 1/2 (pow.f32 (PI.f32) 2)) (.f32 1/6 (.f32 x (pow.f32 (PI.f32) 3)))))))
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(expm1.f32 (*.f32 (PI.f32) x))
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(expm1.f32 (*.f32 (PI.f32) x))
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(expm1.f32 (*.f32 (PI.f32) x))
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(expm1.f32 (*.f32 (PI.f32) x))
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(expm1.f32 (*.f32 (PI.f32) x))
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(expm1.f32 (*.f32 (PI.f32) x))
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(expm1.f32 (*.f32 (PI.f32) x))
(-.f32 (exp.f32 (*.f32 (PI.f32) x)) 1)
(expm1.f32 (*.f32 (PI.f32) x))

prune199.0ms (3.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	156	16	172

Error

0.1b

Counts

172 → 16

Alt Table

Status	Error	Program
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.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))))))
	2.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 1 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) -1/6) (.f32 (pow.f32 x 6) (.f32 (pow.f32 (PI.f32) 6) -1/5040))))))
	1.0b	(.f32 (.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)) (/.f32 (sin.f32 (.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)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	0.9b	(.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)))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.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))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 2)) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (PI.f32))))
✓	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.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))))
	1.3b	(.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))))
	0.9b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32))) (/.f32 1 tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.6b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (.f32 (/.f32 (/.f32 1 x) (PI.f32)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	5.3b	(.f32 (/.f32 (sin.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 5523 to 1630 computations (70.5% saved)

localize47.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.5b	(-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) 1)

series247.0ms (4.7%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

124.0ms

inf

(-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1)

121.0ms

-inf

(-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1)

2.0ms

(-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1)

rewrite83.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

601×	`prod-diff_binary32`
468×	`log-prod_binary32`
163×	`log1p-udef_binary32`
162×	`expm1-udef_binary32`
137×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	207	14
2	2563	14

Stop Event

1×	node limit

Counts

1 → 78

Calls

Call 1

Inputs
(-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) 1)

Outputs

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

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

836×	`distribute-rgt-neg-in_binary32`
487×	`fma-def_binary32`
475×	`cancel-sign-sub-inv_binary32`
290×	`*-commutative_binary32`
274×	`fma-neg_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	206
1	82	206
2	243	202
3	1148	200
4	4116	194

Stop Event

1×	node limit

Counts

90 → 86

Calls

Call 1

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

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

prune227.0ms (4.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	205	8	213
Fresh	4	10	14
Picked	1	0	1
Done	1	0	1
Total	211	18	229

Error

0.1b

Counts

229 → 18

Alt Table

Status	Error	Program
	1.0b	(.f32 (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	4.6b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	1.0b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) 1) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 (sqrt.f32 (+.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) 1)) (sqrt.f32 (+.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))) 1)) -1))
	1.0b	(.f32 (.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)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.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)))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.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))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 2)) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (.f32 x (PI.f32)) (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x 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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))) 1))
	1.0b	(.f32 (.f32 (/.f32 (/.f32 1 x) (PI.f32)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))) (log.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))))
	0.9b	(.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))))
	5.3b	(.f32 (/.f32 (sin.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32))) (/.f32 1 tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 7760 to 2324 computations (70.1% saved)

localize56.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.5b	(-.f32 (exp.f32 (log1p.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))) 1)
✓	0.5b	(log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))
0.0ms	x	@	inf	(log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))
0.0ms	x	@	0	(-.f32 (exp.f32 (log1p.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))) 1)
0.0ms	x	@	-inf	(log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))
0.0ms	x	@	-inf	(-.f32 (exp.f32 (log1p.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))) 1)

rewrite70.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

601×	`prod-diff_binary32`
177×	`log1p-udef_binary32`
176×	`expm1-udef_binary32`
161×	`fma-def_binary32`
152×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	230	28
2	2749	28

Stop Event

1×	node limit

Counts

2 → 163

Calls

Call 1

Inputs
(log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))
(-.f32 (exp.f32 (log1p.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))) 1)

Outputs

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

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

836×	`distribute-rgt-neg-in_binary32`
487×	`fma-def_binary32`
475×	`cancel-sign-sub-inv_binary32`
290×	`*-commutative_binary32`
274×	`fma-neg_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	412
1	82	412
2	243	404
3	1148	400
4	4116	388

Stop Event

1×	node limit

Counts

187 → 92

Calls

Call 1

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

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

prune265.0ms (5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	188	3	191
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	191	18	209

Error

0.1b

Counts

209 → 18

Alt Table

Status	Error	Program
	1.0b	(.f32 (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	4.6b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (-.f32 (exp.f32 (log1p.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))) 1))
	0.9b	(.f32 (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	1.0b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) 1) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (.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))))))) 1))
	0.9b	(.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))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 2)) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (.f32 x (PI.f32)) (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	1.0b	(.f32 (.f32 (/.f32 (/.f32 1 x) (PI.f32)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.0b	(.f32 (.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)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.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)))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))) (log.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))))
	0.9b	(.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))))
	5.3b	(.f32 (/.f32 (sin.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32))) (/.f32 1 tau)) (/.f32 (sin.f32 (.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)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) x))) 1))

Compiler

Compiled 7072 to 2286 computations (67.7% saved)

regimes1.1s (21.2%)

Accuracy

Total 0.5b remaining (79.4%)

Threshold costs 0.5b (79.4%)

Counts

329 → 1

Compiler

Compiled 9286 to 2073 computations (77.7% 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)))

end235.0ms (4.5%)

Stop Event

1×

fuel

Compiler

Compiled 596 to 309 computations (48.2% saved)

Details

analyze3.0ms (0.1%)

sample2.0s (38.1%)

preprocess79.0ms (1.5%)

simplify38.0ms (0.7%)

prune3.0ms (0.1%)

localize35.0ms (0.7%)

series16.0ms (0.3%)

rewrite63.0ms (1.2%)

simplify64.0ms (1.2%)

prune221.0ms (4.2%)

localize42.0ms (0.8%)

series2.0ms (0%)

rewrite42.0ms (0.8%)

simplify30.0ms (0.6%)

prune199.0ms (3.8%)

localize47.0ms (0.9%)

series247.0ms (4.7%)

rewrite83.0ms (1.6%)

simplify31.0ms (0.6%)

prune227.0ms (4.3%)

localize56.0ms (1.1%)

series2.0ms (0%)

rewrite70.0ms (1.3%)

simplify44.0ms (0.8%)

prune265.0ms (5%)

regimes1.1s (21.2%)

simplify2.0ms (0%)

end235.0ms (4.5%)

Profiling