Details

analyze7.0ms (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)

sample3.8s (29.9%)

Results

3.7s

8256×

body

128

valid

Compiler

Compiled 99 to 52 computations (47.5% saved)

simplify62.0ms (0.5%)

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

prune3.0ms (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)

localize76.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series102.0ms (0.8%)

Counts

4 → 72

Calls

4 calls:

62.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
19.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
16.0ms	(.f32 (.f32 x (PI.f32)) tau)
4.0ms	(*.f32 x (PI.f32))

rewrite170.0ms (1.3%)

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 → 113

Calls

4 calls:

166.0ms	(.f32 (.f32 x (PI.f32)) tau)
166.0ms	(*.f32 x (PI.f32))
166.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
166.0ms	(/.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	47
1	213	47
2	3040	47
3	4727	47
4	4687	47
5	5075	47
0	0	0
1	0	0

simplify114.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-neg_binary32`
570×	`distribute-rgt-neg-in_binary32`
556×	`distribute-lft-neg-in_binary32`
489×	`associate-r_binary32`
481×	`associate-l_binary32`

Counts

185 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	1046
1	151	1038
2	485	1026
3	2474	1026
4	4918	1026
5	4979	1026
6	4979	1026

prune405.0ms (3.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	175	19	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	176	19	195

Error

0.1b

Counts

195 → 19

Alt Table

Status	Error	Program
	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))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 x (PI.f32)) 3) (pow.f32 tau 3)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (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)))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.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 (/.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))))
	1.0b	(.f32 (/.f32 (sin.f32 (pow.f32 (sqrt.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 (pow.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) -1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 3)))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))) 3) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	5.5b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1)) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.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))))))
	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))))
	6.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (log.f32 (pow.f32 (exp.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (/.f32 1 (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	0.7b	(.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))))
	1.1b	(.f32 (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) 2) (.f32 (cbrt.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))))

Compiler

Compiled 6139 to 1664 computations (72.9% saved)

localize67.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series61.0ms (0.5%)

Counts

2 → 8

Calls

2 calls:

49.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
12.0ms	(.f32 (PI.f32) (.f32 tau x))

rewrite76.0ms (0.6%)

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 → 58

Calls

2 calls:

74.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
74.0ms	(.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

simplify64.0ms (0.5%)

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

66 → 65

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

prune595.0ms (4.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	156	3	159
Fresh	5	13	18
Picked	1	0	1
Done	0	0	0
Total	162	16	178

Error

0.1b

Counts

178 → 16

Alt Table

Status	Error	Program
	0.7b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (PI.f32)) (/.f32 1 (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 x (PI.f32)) 3) (pow.f32 tau 3)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (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)))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.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 (sqrt.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 (pow.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) -1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (cbrt.f32 (*.f32 x (PI.f32))) 3)))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.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))))))
	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))))
	6.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (log.f32 (pow.f32 (exp.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (/.f32 1 (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) 2) (.f32 (cbrt.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))))

Compiler

Compiled 5129 to 1393 computations (72.8% saved)

localize69.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series177.0ms (1.4%)

Counts

1 → 24

Calls

1 calls:

177.0ms

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

rewrite85.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

573×	`log-prod_binary32`
468×	`prod-diff_binary32`
184×	`expm1-udef_binary32`
184×	`log1p-udef_binary32`
170×	`log-pow_binary32`

Counts

1 → 57

Calls

1 calls:

82.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	208	20
2	2631	20
3	5248	20
0	0	0
1	0	0

simplify76.0ms (0.6%)

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

81 → 65

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

prune415.0ms (3.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	200	8	208
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	209	15	224

Error

0.0b

Counts

224 → 15

Alt Table

Status	Error	Program
	0.9b	(.f32 (pow.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) -1) (.f32 (/.f32 1 (sqrt.f32 (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (sqrt.f32 (*.f32 x (PI.f32))))))
	0.7b	(.f32 (pow.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) -1) (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	0.7b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (PI.f32)) (/.f32 1 (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 x (PI.f32)) 3) (pow.f32 tau 3)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (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)))
	1.0b	(.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))))) (log.f32 (sqrt.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 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) 2) (.f32 (cbrt.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))))
	0.7b	(.f32 (pow.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) -1) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3)))) (*.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))))
▶	0.7b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (PI.f32))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.f32 (pow.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) -1) (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))
	0.9b	(.f32 (.f32 (/.f32 1 (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.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))))
	0.7b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.3b	(.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))))) (log.f32 (cbrt.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))))

Compiler

Compiled 6754 to 1919 computations (71.6% saved)

localize72.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series96.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

52.0ms	(/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (*.f32 x (PI.f32))) tau)
44.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (*.f32 x (PI.f32)))

rewrite153.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

617×	`log-prod_binary32`
495×	`prod-diff_binary32`
183×	`expm1-udef_binary32`
183×	`log1p-udef_binary32`
167×	`log-pow_binary32`

Counts

2 → 100

Calls

2 calls:

148.0ms	(/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (*.f32 x (PI.f32))) tau)
148.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (*.f32 x (PI.f32)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	37
1	193	37
2	2785	37
3	5738	37
0	0	0
1	0	0

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

992×	`fma-neg_binary32`
899×	`distribute-rgt-neg-in_binary32`
800×	`associate-r_binary32`
733×	`associate-l_binary32`
203×	`*-commutative_binary32`

Counts

148 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	60	1120
1	178	1112
2	616	1096
3	3492	1096
4	5661	1096

prune432.0ms (3.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	225	2	227
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	227	15	242

Error

0.0b

Counts

242 → 15

Alt Table

Status	Error	Program
	0.9b	(.f32 (pow.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) -1) (.f32 (/.f32 1 (sqrt.f32 (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (sqrt.f32 (*.f32 x (PI.f32))))))
	0.7b	(.f32 (pow.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) -1) (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	0.7b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (PI.f32)) (/.f32 1 (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 x (PI.f32)) 3) (pow.f32 tau 3)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (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)))
	0.7b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (PI.f32)))))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (PI.f32))))))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))))) (log.f32 (sqrt.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 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) 2) (.f32 (cbrt.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))))
	0.9b	(.f32 (pow.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) -1) (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))
	0.7b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (PI.f32)))))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (/.f32 1 (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.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))))
	1.3b	(.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))))) (log.f32 (cbrt.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))))
	0.7b	(.f32 (pow.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) -1) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 x 3)))) (*.f32 x (PI.f32))))

Compiler

Compiled 6758 to 1668 computations (75.3% saved)

regimes5.1s (40%)

Accuracy

Total 0.6b remaining (79.9%)

Threshold costs 0.6b (79.9%)

Counts

463 → 1

Compiler

Compiled 51924 to 26948 computations (48.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	16	40
2	16	40

end390.0ms (3%)

Compiler: Compiled 539 to 253 computations (53.1% saved)

Details

analyze7.0ms (0.1%)

sample3.8s (29.9%)

simplify62.0ms (0.5%)

prune3.0ms (0%)

localize76.0ms (0.6%)

series102.0ms (0.8%)

rewrite170.0ms (1.3%)

simplify114.0ms (0.9%)

prune405.0ms (3.2%)

localize67.0ms (0.5%)

series61.0ms (0.5%)

rewrite76.0ms (0.6%)

simplify64.0ms (0.5%)

prune595.0ms (4.6%)

localize69.0ms (0.5%)

series177.0ms (1.4%)

rewrite85.0ms (0.7%)

simplify76.0ms (0.6%)

prune415.0ms (3.2%)

localize72.0ms (0.6%)

series96.0ms (0.8%)

rewrite153.0ms (1.2%)

simplify88.0ms (0.7%)

prune432.0ms (3.4%)

regimes5.1s (40%)

simplify3.0ms (0%)

end390.0ms (3%)

Profiling