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)

sample2.6s (41.3%)

Results

2.5s

8256×

body

128

valid

Compiler

Compiled 99 to 52 computations (47.5% saved)

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/l/_binary32`
455×	`associate-/l*_binary32`
281×	`times-frac_binary32`
257×	`associate-/r/_binary32`
154×	`associate-*l/_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	24	36
2	80	36
3	299	36
4	822	36
5	1265	36
6	1211	36
7	1239	36
8	1247	36
9	1251	36
10	1253	36
11	1219	36
12	1217	36

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.6b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 69 to 30 computations (56.5% saved)

localize36.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series49.0ms (0.8%)

Counts

4 → 72

Calls

4 calls:

29.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
9.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
8.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
2.0ms	(*.f32 x (PI.f32))

rewrite124.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

720×	`prod-diff_binary32`
487×	`fma-udef_binary32`
203×	`expm1-udef_binary32`
203×	`log1p-udef_binary32`
201×	`fma-neg_binary32`

Counts

4 → 121

Calls

4 calls:

121.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
121.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
121.0ms	(*.f32 x (PI.f32))
121.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	49
1	213	49
2	3040	49
3	4727	49
4	4687	49
5	5075	49
0	0	0
1	0	0

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

839×	`distribute-rgt-neg-in_binary32`
473×	`fma-neg_binary32`
440×	`distribute-lft-neg-in_binary32`
343×	`sub-neg_binary32`
332×	`*-commutative_binary32`

Counts

193 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	1330
1	242	1314
2	861	1298
3	2184	1298
4	3988	1298
5	4988	1298
6	4949	1298

prune212.0ms (3.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	181	15	196
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	15	197

Error

0.1b

Counts

197 → 15

Alt Table

Status	Error	Program
	1.1b	(.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 (.f32 x (PI.f32)) tau)) 2)) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (cbrt.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	5.3b	(.f32 (/.f32 (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) 1) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	7.6b	(.f32 (/.f32 (sin.f32 (.f32 (log.f32 (pow.f32 (exp.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) 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 (+.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))))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2)) (*.f32 x (PI.f32))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) 2)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	3.9b	(.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) -1/6 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) 1) (/.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 (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)))
	0.9b	(.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))))
	1.1b	(.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))))

Compiler

Compiled 6140 to 1669 computations (72.8% saved)

localize40.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series33.0ms (0.5%)

Counts

2 → 8

Calls

2 calls:

27.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
6.0ms	(.f32 (PI.f32) (.f32 tau x))

rewrite53.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

879×	`log1p-expm1-u_binary32`
879×	`expm1-log1p-u_binary32`
511×	`prod-diff_binary32`
86×	`add-sqr-sqrt_binary32`
80×	`associate-r_binary32`

Counts

2 → 60

Calls

2 calls:

52.0ms	(.f32 (PI.f32) (.f32 tau x))
52.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	166	28
2	2243	28
3	6341	28
0	0	0
1	0	0

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

755×	`fma-neg_binary32`
726×	`cancel-sign-sub-inv_binary32`
705×	`fma-def_binary32`
440×	`distribute-rgt-neg-in_binary32`
426×	`distribute-lft-neg-in_binary32`

Counts

68 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	268
1	98	260
2	325	252
3	1826	248
4	4253	248
5	5052	248

prune195.0ms (3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	158	7	165
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	164	16	180

Error

0.1b

Counts

180 → 16

Alt Table

Status	Error	Program
	1.1b	(.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 (.f32 x (PI.f32)) tau)) 2)) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (cbrt.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	5.3b	(.f32 (/.f32 (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) 1) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	7.6b	(.f32 (/.f32 (sin.f32 (.f32 (log.f32 (pow.f32 (exp.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) 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 (+.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))))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau 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))))))
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) 2) (PI.f32)) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	6.2b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (-.f32 (exp.f32 (log1p.f32 (*.f32 x (PI.f32)))) 1)))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2)) (*.f32 x (PI.f32))))
	0.9b	(.f32 (log.f32 (exp.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))))
▶	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.9b	(.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) -1/6 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1)) (/.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 (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)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3)) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (.f32 (/.f32 1 (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))))

Compiler

Compiled 5341 to 1482 computations (72.3% saved)

localize50.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series26.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

26.0ms

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

rewrite52.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

855×	`prod-diff_binary32`
529×	`log-prod_binary32`
170×	`expm1-udef_binary32`
170×	`log1p-udef_binary32`
158×	`log-pow_binary32`

Counts

1 → 46

Calls

1 calls:

50.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	183	20
2	2355	20
3	5368	20
0	0	0
1	0	0

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

723×	`cancel-sign-sub-inv_binary32`
705×	`fma-def_binary32`
687×	`fma-neg_binary32`
435×	`distribute-rgt-neg-in_binary32`
421×	`distribute-lft-neg-in_binary32`

Counts

70 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	588
1	108	580
2	345	572
3	1868	568
4	4233	568
5	4976	568

prune175.0ms (2.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	169	14	183

Error

0.1b

Counts

183 → 14

Alt Table

Status	Error	Program
	1.1b	(.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 (.f32 x (PI.f32)) tau)) 2)) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (cbrt.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	5.3b	(.f32 (/.f32 (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) 1) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	0.7b	(.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	3.9b	(.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) -1/6 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (/.f32 1 (PI.f32)) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau 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))))))
	1.0b	(.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) 2) (PI.f32)) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	6.2b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (-.f32 (exp.f32 (log1p.f32 (*.f32 x (PI.f32)))) 1)))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2)) (*.f32 x (PI.f32))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 tau x))) 3)) (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.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 (+.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))))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.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)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3)) (*.f32 x (PI.f32))))

Compiler

Compiled 5570 to 1477 computations (73.5% saved)

localize45.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series27.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

27.0ms

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

rewrite82.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

643×	`prod-diff_binary32`
531×	`log-prod_binary32`
175×	`expm1-udef_binary32`
175×	`log1p-udef_binary32`
163×	`log-pow_binary32`

Counts

1 → 34

Calls

1 calls:

81.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	200	20
2	2416	20
3	4933	20
4	5293	20
0	0	0
1	0	0

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

723×	`cancel-sign-sub-inv_binary32`
705×	`fma-def_binary32`
687×	`fma-neg_binary32`
435×	`distribute-rgt-neg-in_binary32`
421×	`distribute-lft-neg-in_binary32`

Counts

58 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	588
1	108	580
2	345	572
3	1868	568
4	4233	568
5	4976	568

prune177.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	152	3	155
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	157	12	169

Error

0.0b

Counts

169 → 12

Alt Table

Status	Error	Program
	1.1b	(.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 (.f32 x (PI.f32)) tau)) 2)) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (cbrt.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	5.3b	(.f32 (/.f32 (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) 1) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))
	1.0b	(.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) 2) (PI.f32)) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 tau x))) 3)) (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.9b	(.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) -1/6 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (/.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2)) (.f32 x (PI.f32))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.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))))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau 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))))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.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)))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	6.2b	(.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (-.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1)))

Compiler

Compiled 4636 to 1429 computations (69.2% saved)

regimes1.9s (29.8%)

Accuracy

Total 0.5b remaining (74.6%)

Threshold costs 0.5b (74.6%)

Counts

392 → 1

Compiler

Compiled 45824 to 24664 computations (46.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	18	40
2	18	40

end178.0ms (2.8%)

Compiler: Compiled 447 to 251 computations (43.8% saved)

Details

analyze3.0ms (0.1%)

sample2.6s (41.3%)

simplify44.0ms (0.7%)

prune2.0ms (0%)

localize36.0ms (0.6%)

series49.0ms (0.8%)

rewrite124.0ms (1.9%)

simplify93.0ms (1.5%)

prune212.0ms (3.3%)

localize40.0ms (0.6%)

series33.0ms (0.5%)

rewrite53.0ms (0.8%)

simplify46.0ms (0.7%)

prune195.0ms (3%)

localize50.0ms (0.8%)

series26.0ms (0.4%)

rewrite52.0ms (0.8%)

simplify51.0ms (0.8%)

prune175.0ms (2.7%)

localize45.0ms (0.7%)

series27.0ms (0.4%)

rewrite82.0ms (1.3%)

simplify52.0ms (0.8%)

prune177.0ms (2.8%)

regimes1.9s (29.8%)

simplify2.0ms (0%)

end178.0ms (2.8%)

Profiling