Details

analyze566.0ms (6.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	40.6%	9.5%	7
50%	39%	11%	8
50%	33.6%	16.5%	9
50%	32.4%	17.7%	10
50%	29.5%	20.6%	11
50%	28.8%	21.3%	12
50%	27.3%	22.8%	13
50%	26.9%	23.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample6.0s (66.7%)

Results

2.9s	4201×	body	1024	valid
1.0s	1926×	body	1024	invalid
827.0ms	2090×	body	512	valid
359.0ms	1006×	body	512	invalid
272.0ms	1049×	body	256	valid
229.0ms	210×	body	2048	valid
131.0ms	792×	body	128	invalid
129.0ms	545×	body	256	invalid
101.0ms	706×	body	128	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

430×	`rules-20_binary64`
425×	`rules-15_binary64`
405×	`rules-5_binary64`
318×	`fma-neg_binary64`
262×	`rules-21_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	23	18
2	52	18
3	117	18
4	345	18
5	1398	17
6	3949	17
7	4531	17
8	4938	17

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

42.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	42.5b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 50 to 35 computations (30% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 im)
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	6.0b	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series17.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

14.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
2.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
1.0ms	(exp.f64 im)

rewrite123.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

629×	`prod-diff_binary64`
296×	`egg-rr`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
114×	`add-sqr-sqrt_binary64`

Counts

3 → 296

Calls

3 calls:

112.0ms	(exp.f64 im)
112.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
112.0ms	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	258	31
2	3316	31
3	5079	31
0	0	0
1	0	0

simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

851×	`rules-13_binary64`
653×	`rules-11_binary64`
550×	`fma-neg_binary64`
391×	`rules-20_binary64`
297×	`rules-21_binary64`

Counts

332 → 331

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	771
1	364	733
2	1656	732
3	6495	732

prune207.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	329	2	331
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	329	3	332

Error

0.1b

Counts

332 → 3

Alt Table

Status	Error	Program
✓	42.5b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
	42.5b	(/.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (/.f64 1 (*.f64 1/2 (sin.f64 re))))
▶	0.5b	(neg.f64 (.f64 (sin.f64 re) (+.f64 im (.f64 (pow.f64 im 3) 1/6))))

Compiler

Compiled 11719 to 5479 computations (53.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (sin.f64 re) (+.f64 im (.f64 (pow.f64 im 3) 1/6)))
✓	0.1b	(*.f64 (pow.f64 im 3) 1/6)

series21.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

18.0ms	(.f64 (sin.f64 re) (+.f64 im (.f64 (pow.f64 im 3) 1/6)))
3.0ms	(*.f64 (pow.f64 im 3) 1/6)

rewrite78.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

914×	`fma-neg_binary64`
661×	`prod-diff_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
173×	`egg-rr`

Counts

2 → 173

Calls

2 calls:

75.0ms	(.f64 (sin.f64 re) (+.f64 im (.f64 (pow.f64 im 3) 1/6)))
75.0ms	(*.f64 (pow.f64 im 3) 1/6)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	241	20
2	3039	20
3	5530	20
0	0	0
1	0	0

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
456×	`fma-neg_binary64`
402×	`rules-11_binary64`
384×	`rules-13_binary64`
233×	`rules-20_binary64`

Counts

209 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	527
1	169	507
2	866	491
3	4938	491
4	5018	491

prune181.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	185	7	192

Error

0.0b

Counts

192 → 7

Alt Table

Status	Error	Program
	1.5b	(neg.f64 (fma.f64 (cbrt.f64 (fma.f64 (pow.f64 im 3) 1/6 im)) (*.f64 (sin.f64 re) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 im 3) 1/6 im)) 2)) 0))
	1.4b	(neg.f64 (fma.f64 (cbrt.f64 (sin.f64 re)) (*.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (pow.f64 (cbrt.f64 (sin.f64 re)) 2)) 0))
▶	0.6b	(neg.f64 (/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (/.f64 1 (sin.f64 re))))
✓	42.5b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
	42.5b	(/.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (/.f64 1 (*.f64 1/2 (sin.f64 re))))
✓	0.5b	(neg.f64 (.f64 (sin.f64 re) (+.f64 im (.f64 (pow.f64 im 3) 1/6))))
	34.4b	(neg.f64 (fma.f64 (sqrt.f64 (sin.f64 re)) (*.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (sqrt.f64 (sin.f64 re))) 0))

Compiler

Compiled 4456 to 2972 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sin.f64 re))
✓	0.2b	(/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (/.f64 1 (sin.f64 re)))

series21.0ms (0.2%)

Counts

2 → 28

Calls

2 calls:

16.0ms	(/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (/.f64 1 (sin.f64 re)))
5.0ms	(/.f64 1 (sin.f64 re))

rewrite95.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

680×	`fma-neg_binary64`
369×	`fma-def_binary64`
272×	`prod-diff_binary64`
177×	`expm1-udef_binary64`
177×	`log1p-udef_binary64`

Counts

2 → 126

Calls

2 calls:

93.0ms	(/.f64 1 (sin.f64 re))
93.0ms	(/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (/.f64 1 (sin.f64 re)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	246	19
2	2739	19
3	4968	19
4	4964	19
0	0	0
1	0	0

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
465×	`rules-13_binary64`
456×	`fma-neg_binary64`
402×	`rules-11_binary64`
261×	`rules-20_binary64`

Counts

154 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	498
1	205	472
2	1016	456
3	4879	456
4	5002	456

prune133.0ms (1.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	146	7	153

Error

0.0b

Counts

153 → 7

Alt Table

Status	Error	Program
	1.4b	(neg.f64 (fma.f64 (cbrt.f64 (sin.f64 re)) (*.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (pow.f64 (cbrt.f64 (sin.f64 re)) 2)) 0))
▶	1.3b	(neg.f64 (/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) -1) (pow.f64 (cbrt.f64 (sin.f64 re)) -1))))
	4.0b	(neg.f64 (/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (*.f64 (/.f64 1 (cbrt.f64 (sin.f64 re))) (cbrt.f64 (pow.f64 (sin.f64 re) -2)))))
✓	42.5b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.6b	(neg.f64 (/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (/.f64 1 (sin.f64 re))))
	42.5b	(/.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (/.f64 1 (*.f64 1/2 (sin.f64 re))))
✓	0.5b	(neg.f64 (.f64 (sin.f64 re) (+.f64 im (.f64 (pow.f64 im 3) 1/6))))

Compiler

Compiled 3071 to 2092 computations (31.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) -1)
✓	0.4b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) -1) (pow.f64 (cbrt.f64 (sin.f64 re)) -1))
✓	0.5b	(pow.f64 (cbrt.f64 (sin.f64 re)) 2)
✓	0.6b	(cbrt.f64 (sin.f64 re))

series403.0ms (4.5%)

Counts

4 → 48

Calls

4 calls:

146.0ms	(pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) -1)
126.0ms	(pow.f64 (cbrt.f64 (sin.f64 re)) 2)
124.0ms	(cbrt.f64 (sin.f64 re))
6.0ms	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) -1) (pow.f64 (cbrt.f64 (sin.f64 re)) -1))

rewrite71.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

767×	`log1p-expm1-u_binary64`
767×	`expm1-log1p-u_binary64`
199×	`prod-diff_binary64`
182×	`egg-rr`
88×	`add-sqr-sqrt_binary64`

Counts

4 → 182

Calls

4 calls:

66.0ms	(pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) -1)
66.0ms	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) -1) (pow.f64 (cbrt.f64 (sin.f64 re)) -1))
66.0ms	(pow.f64 (cbrt.f64 (sin.f64 re)) 2)
66.0ms	(cbrt.f64 (sin.f64 re))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	232	23
2	2321	23
3	5290	23
0	0	0
1	0	0

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

856×	`rules-13_binary64`
624×	`rules-20_binary64`
366×	`rules-21_binary64`
313×	`rules-14-rev_binary64`
231×	`fma-def_binary64`

Counts

230 → 217

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	547
1	213	537
2	637	535
3	2334	535
4	5325	535

prune229.0ms (2.5%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	257	8	265

Error

0.0b

Counts

265 → 8

Alt Table

Status	Error	Program
	1.4b	(neg.f64 (fma.f64 (cbrt.f64 (sin.f64 re)) (*.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (pow.f64 (cbrt.f64 (sin.f64 re)) 2)) 0))
✓	1.3b	(neg.f64 (/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) -1) (pow.f64 (cbrt.f64 (sin.f64 re)) -1))))
	4.0b	(neg.f64 (/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (*.f64 (/.f64 1 (cbrt.f64 (sin.f64 re))) (cbrt.f64 (pow.f64 (sin.f64 re) -2)))))
✓	42.5b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.6b	(neg.f64 (/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (/.f64 1 (sin.f64 re))))
	42.5b	(/.f64 (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (/.f64 1 (*.f64 1/2 (sin.f64 re))))
✓	0.5b	(neg.f64 (.f64 (sin.f64 re) (+.f64 im (.f64 (pow.f64 im 3) 1/6))))
	20.9b	(neg.f64 (/.f64 (fma.f64 (pow.f64 im 3) 1/6 im) (/.f64 (pow.f64 (pow.f64 (sin.f64 re) -1) 3) (+.f64 (pow.f64 (sin.f64 re) -2) (+.f64 0 (*.f64 (pow.f64 (sin.f64 re) -1) 0))))))

Compiler

Compiled 7135 to 4747 computations (33.5% saved)

regimes423.0ms (4.7%)

Accuracy

Total 0.8b remaining (88.9%)

Threshold costs 0.8b (88.9%)

Counts

66 → 1

Compiler

Compiled 8205 to 6081 computations (25.9% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	10	15

end137.0ms (1.5%)

Compiler: Compiled 173 to 131 computations (24.3% saved)

Details

analyze566.0ms (6.2%)

sample6.0s (66.7%)

simplify67.0ms (0.7%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series17.0ms (0.2%)

rewrite123.0ms (1.4%)

simplify53.0ms (0.6%)

prune207.0ms (2.3%)

localize7.0ms (0.1%)

series21.0ms (0.2%)

rewrite78.0ms (0.9%)

simplify54.0ms (0.6%)

prune181.0ms (2%)

localize8.0ms (0.1%)

series21.0ms (0.2%)

rewrite95.0ms (1.1%)

simplify50.0ms (0.6%)

prune133.0ms (1.5%)

localize13.0ms (0.1%)

series403.0ms (4.5%)

rewrite71.0ms (0.8%)

simplify45.0ms (0.5%)

prune229.0ms (2.5%)

regimes423.0ms (4.7%)

simplify1.0ms (0%)

end137.0ms (1.5%)

Profiling