Details

analyze3.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample2.2s (32.7%)

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))))

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 145 to 72 computations (50.3% saved)

localize34.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(sin.f32 (.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))

series49.0ms (0.7%)

Counts

4 → 72

Calls

4 calls:

29.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
10.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
8.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
2.0ms	(*.f32 x (PI.f32))

rewrite129.0ms (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 → 117

Calls

4 calls:

126.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
126.0ms	(*.f32 x (PI.f32))
126.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
126.0ms	(/.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

prune268.0ms (3.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	255	15	270
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	256	15	271

Error

0.1b

Counts

271 → 15

Alt Table

Status	Error	Program
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (*.f32 x (PI.f32))))
	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))))))
	5.9b	(.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 (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)))
	0.8b	(.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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (sqrt.f32 (*.f32 x (PI.f32))) 2)))
	0.8b	(.f32 (log.f32 (+.f32 1 (expm1.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))))
	1.2b	(.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))))
	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 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 1 (.f32 x (PI.f32))))))
	5.9b	(.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))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	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))
▶	0.7b	(.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))))
	1.2b	(.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) 2) (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (cbrt.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))))
	3.8b	(.f32 (-.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 x (PI.f32))) (.f32 x (PI.f32))))

Compiler

Compiled 7708 to 1669 computations (78.3% saved)

localize38.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series50.0ms (0.7%)

Counts

4 → 32

Calls

4 calls:

29.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
9.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
6.0ms	(.f32 (PI.f32) (.f32 tau x))
5.0ms	(*.f32 x (PI.f32))

rewrite78.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

763×	`prod-diff_binary32`
221×	`log1p-udef_binary32`
121×	`add-sqr-sqrt_binary32`
113×	`egg-rr`
111×	`add-log-exp_binary32`

Counts

4 → 113

Calls

4 calls:

75.0ms	(.f32 (PI.f32) (.f32 tau x))
75.0ms	(*.f32 x (PI.f32))
75.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
75.0ms	(/.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	11	47
1	233	47
2	3286	47
3	5016	47
0	0	0
1	0	0

prune273.0ms (4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	186	16	202

Error

0.1b

Counts

202 → 16

Alt Table

Status	Error	Program
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) x))) 2) (sqrt.f32 (.f32 (PI.f32) x))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) x))) (sqrt.f32 (.f32 (PI.f32) x)))))
▶	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (*.f32 x (PI.f32))))
	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))))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x))) 3))
	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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (sqrt.f32 (*.f32 x (PI.f32))) 2)))
	3.8b	(.f32 (-.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 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.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))))
	0.8b	(.f32 (log.f32 (+.f32 1 (expm1.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))))
	1.2b	(.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))))
	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 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 1 (.f32 x (PI.f32))))))
	5.9b	(.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))))
	5.9b	(.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))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	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))
	1.2b	(.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) 2) (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (cbrt.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))))

Compiler

Compiled 5793 to 1445 computations (75.1% saved)

localize52.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f32 x (PI.f32))
✓	0.4b	(/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (.f32 x (PI.f32)))
✓	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
✓	1.0b	(pow.f32 (PI.f32) 3)

series53.0ms (0.8%)

Counts

4 → 48

Calls

4 calls:

31.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
20.0ms	(/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (.f32 x (PI.f32)))
2.0ms	(*.f32 x (PI.f32))
0.0ms	(pow.f32 (PI.f32) 3)

rewrite81.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

828×	`prod-diff_binary32`
146×	`add-sqr-sqrt_binary32`
137×	`add-cbrt-cube_binary32`
137×	`log1p-expm1-u_binary32`
137×	`expm1-log1p-u_binary32`

Counts

4 → 118

Calls

4 calls:

78.0ms	(*.f32 x (PI.f32))
78.0ms	(/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (.f32 x (PI.f32)))
78.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
78.0ms	(pow.f32 (PI.f32) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	44
1	301	44
2	3872	44
3	5265	44
0	0	0
1	0	0

prune278.0ms (4.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	217	17	234

Error

0.1b

Counts

234 → 17

Alt Table

Status	Error	Program
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) x))) 2) (sqrt.f32 (.f32 (PI.f32) x))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) x))) (sqrt.f32 (.f32 (PI.f32) x)))))
	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))))))
	0.8b	(.f32 (log.f32 (+.f32 1 (expm1.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))))
▶	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (exp.f32 (.f32 3 (log.f32 (PI.f32))))))) (.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x))) 3))
	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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (sqrt.f32 (*.f32 x (PI.f32))) 2)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32))))) (.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) x))) 1) (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))))
	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))
	3.8b	(.f32 (-.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 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.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))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (pow.f32 (cbrt.f32 (*.f32 (PI.f32) x)) 3)))
	1.2b	(.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))))
	5.9b	(.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))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) 2) (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (cbrt.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))))

Compiler

Compiled 7391 to 2889 computations (60.9% saved)

localize65.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (exp.f32 (.f32 3 (log.f32 (PI.f32))))))) (*.f32 x (PI.f32)))
✓	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
✓	1.0b	(log.f32 (PI.f32))
✓	1.6b	(exp.f32 (*.f32 3 (log.f32 (PI.f32))))

series53.0ms (0.8%)

Counts

4 → 36

Calls

4 calls:

34.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
18.0ms	(/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (exp.f32 (.f32 3 (log.f32 (PI.f32))))))) (*.f32 x (PI.f32)))
0.0ms	(exp.f32 (*.f32 3 (log.f32 (PI.f32))))
0.0ms	(log.f32 (PI.f32))

rewrite86.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

828×	`prod-diff_binary32`
169×	`add-sqr-sqrt_binary32`
160×	`add-cbrt-cube_binary32`
160×	`add-log-exp_binary32`
160×	`log1p-expm1-u_binary32`

Counts

4 → 127

Calls

4 calls:

84.0ms	(/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (exp.f32 (.f32 3 (log.f32 (PI.f32))))))) (*.f32 x (PI.f32)))
84.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
83.0ms	(log.f32 (PI.f32))
83.0ms	(exp.f32 (*.f32 3 (log.f32 (PI.f32))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	56
1	349	43
2	4214	43
3	5597	43
0	0	0
1	0	0

prune172.0ms (2.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	163	17	180

Error

0.1b

Counts

180 → 17

Alt Table

Status	Error	Program
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) x))) 2) (sqrt.f32 (.f32 (PI.f32) x))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) x))) (sqrt.f32 (.f32 (PI.f32) x)))))
	0.9b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 (PI.f32) x)) (/.f32 1 tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (exp.f32 (.f32 3 (log.f32 (PI.f32))))))) (.f32 x (PI.f32))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 (.f32 (PI.f32) x) tau)))) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (exp.f32 (.f32 3 (log.f32 (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 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (pow.f32 (cbrt.f32 (*.f32 (PI.f32) x)) 3)))
	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))))
	1.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (exp.f32 (.f32 3 (-.f32 (exp.f32 (log1p.f32 (log.f32 (PI.f32)))) 1)))))) (.f32 x (PI.f32))))
	1.0b	(.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 (sqrt.f32 (*.f32 x (PI.f32))) 2)))
	3.8b	(.f32 (-.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 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (pow.f32 (pow.f32 (PI.f32) 3) 3) 1/3)))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log.f32 (+.f32 1 (expm1.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))))
	1.2b	(.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))))
	5.9b	(.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))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	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 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (exp.f32 1) (.f32 3 (log.f32 (PI.f32))))))) (.f32 x (PI.f32))))
	1.2b	(.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) 2) (sqrt.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (cbrt.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))))

Compiler

Compiled 5554 to 2116 computations (61.9% saved)

regimes2.6s (37.7%)

Accuracy

Total 0.5b remaining (76.9%)

Threshold costs 0.5b (76.9%)

Counts

407 → 1

Compiler

Compiled 47864 to 26236 computations (45.2% 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

end265.0ms (3.9%)

Compiler: Compiled 606 to 341 computations (43.7% saved)

Details

analyze3.0ms (0%)

sample2.2s (32.7%)

localize34.0ms (0.5%)

series49.0ms (0.7%)

rewrite129.0ms (1.9%)

prune268.0ms (3.9%)

localize38.0ms (0.6%)

series50.0ms (0.7%)

rewrite78.0ms (1.1%)

prune273.0ms (4%)

localize52.0ms (0.8%)

series53.0ms (0.8%)

rewrite81.0ms (1.2%)

prune278.0ms (4.1%)

localize65.0ms (0.9%)

series53.0ms (0.8%)

rewrite86.0ms (1.3%)

prune172.0ms (2.5%)

regimes2.6s (37.7%)

simplify2.0ms (0%)

end265.0ms (3.9%)

Profiling