Details

analyze210.0ms (4.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
74.9%	18.7%	6.3%	6
74.9%	18.7%	6.3%	7
74.9%	15.6%	9.5%	8
74.9%	15.6%	9.5%	9
74.9%	14%	11%	10
74.9%	14%	11%	11
74.9%	13.3%	11.8%	12
74.9%	13.3%	11.8%	13
74.9%	12.9%	12.2%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample2.1s (48.7%)

Results

732.0ms	1387×	body	1024	valid
648.0ms	5774×	body	128	valid
302.0ms	650×	body	1024	invalid
212.0ms	727×	body	512	valid
88.0ms	306×	body	512	invalid
69.0ms	363×	body	256	valid
31.0ms	163×	body	256	invalid
25.0ms	184×	body	128	invalid
6.0ms	5×	body	2048	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

prune5.0ms (0.1%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 re)
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))

series9.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

8.0ms	(*.f64 (exp.f64 re) (cos.f64 im))
1.0ms	(exp.f64 re)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`pow1_binary64`

Counts

2 → 33

Calls

2 calls:

4.0ms	(*.f64 (exp.f64 re) (cos.f64 im))
1.0ms	(exp.f64 re)

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Rules

943×	`fma-neg_binary64`
594×	`cancel-sign-sub-inv_binary64`
333×	`distribute-rgt-neg-in_binary64`
283×	`*-commutative_binary64`
241×	`associate-l_binary64`

Counts

45 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	83	511
1	194	470
2	543	447
3	1476	432
4	2475	430
5	4462	430
6	4831	430
7	4879	430

prune38.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	3	65

Error

0.0b

Counts

65 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
▶	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im)))
	0.2b	(cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im))))

Compiler

Compiled 753 to 300 computations (60.2% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f64 re)
✓	0.0b	(sqrt.f64 (exp.f64 re))
✓	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im)))
✓	0.0b	(*.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im))

series24.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

14.0ms	(*.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im))
8.0ms	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im)))
2.0ms	(sqrt.f64 (exp.f64 re))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
11×	`pow1_binary64`
10×	`sqrt-prod_binary64`
10×	`*-un-lft-identity_binary64`

Counts

3 → 65

Calls

3 calls:

8.0ms	(*.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im))
8.0ms	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im)))
1.0ms	(sqrt.f64 (exp.f64 re))

simplify109.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

844×	`fma-neg_binary64`
551×	`cancel-sign-sub-inv_binary64`
401×	`fma-def_binary64`
305×	`*-commutative_binary64`
276×	`distribute-rgt-neg-in_binary64`

Counts

101 → 123

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	129	1306
1	315	1215
2	940	1159
3	1872	1126
4	3249	1118
5	4522	1118
6	4813	1118
7	4920	1118

prune120.0ms (2.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	193	3	196

Error

0.0b

Counts

196 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
✓	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im)))
▶	0.2b	(cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im))))

Compiler

Compiled 2975 to 920 computations (69.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
✓	0.1b	(.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im)))
✓	0.2b	(.f64 (.f64 (exp.f64 re) (cos.f64 im)) (*.f64 (exp.f64 re) (cos.f64 im)))
✓	0.2b	(cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im))))

series64.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

33.0ms

(*.f64 (*.f64 (*.f64 (exp.f64 re) (cos.f64 im)) (*.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im)))

23.0ms

(*.f64 (*.f64 (exp.f64 re) (cos.f64 im)) (*.f64 (exp.f64 re) (cos.f64 im)))

8.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 (exp.f64 re) (cos.f64 im)) (*.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im))))

rewrite52.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

197×	`pow1_binary64`
86×	`pow-prod-down_binary64`
65×	`add-cbrt-cube_binary64`
42×	`cbrt-unprod_binary64`
39×	`prod-exp_binary64`

Counts

3 → 126

Calls

3 calls:

16.0ms

(*.f64 (*.f64 (*.f64 (exp.f64 re) (cos.f64 im)) (*.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im)))

14.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 (exp.f64 re) (cos.f64 im)) (*.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im))))

8.0ms

(*.f64 (*.f64 (exp.f64 re) (cos.f64 im)) (*.f64 (exp.f64 re) (cos.f64 im)))

simplify118.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

633×	`fma-def_binary64`
513×	`*-commutative_binary64`
441×	`fma-neg_binary64`
429×	`cancel-sign-sub-inv_binary64`
282×	`associate-l_binary64`

Counts

198 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	3386
1	435	2155
2	1473	2008
3	3451	2004
4	4906	2004
5	4972	2004

prune205.0ms (4.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	275	1	276
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	275	4	279

Error

0.0b

Counts

279 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
✓	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im)))
▶	0.2b	(expm1.f64 (log1p.f64 (cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im))))))
✓	0.2b	(cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im))))

Compiler

Compiled 6532 to 1659 computations (74.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im)))
✓	0.2b	(log1p.f64 (cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im)))))
	0.2b	(.f64 (.f64 (exp.f64 re) (cos.f64 im)) (*.f64 (exp.f64 re) (cos.f64 im)))
	0.2b	(cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im))))

series556.0ms (12.6%)

Counts

1 → 24

Calls

1 calls:

556.0ms

(log1p.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (exp.f64 re) (cos.f64 im)) (*.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`expm1-log1p-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(log1p.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (exp.f64 re) (cos.f64 im)) (*.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im)))))

simplify37.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

771×	`times-frac_binary64`
504×	`associate-/l*_binary64`
384×	`associate-l_binary64`
334×	`associate-/r*_binary64`
210×	`fma-def_binary64`

Counts

35 → 36

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1042
1	306	830
2	1063	739
3	5056	739

prune189.0ms (4.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	183	4	187

Error

0.0b

Counts

187 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
✓	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im)))
✓	0.2b	(expm1.f64 (log1p.f64 (cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im))))))
✓	0.2b	(cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 re) (cos.f64 im)) (.f64 (exp.f64 re) (cos.f64 im))) (*.f64 (exp.f64 re) (cos.f64 im))))

Compiler

Compiled 4754 to 1686 computations (64.5% saved)

regimes314.0ms (7.1%)

Accuracy

Total 0.0b remaining (52.3%)

Threshold costs 0.0b (52.3%)

Counts

56 → 1

Compiler

Compiled 4187 to 2930 computations (30% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end55.0ms (1.3%)

Compiler: Compiled 75 to 40 computations (46.7% saved)

Details

analyze210.0ms (4.8%)

sample2.1s (48.7%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify87.0ms (2%)

prune38.0ms (0.9%)

localize6.0ms (0.1%)

series24.0ms (0.6%)

rewrite21.0ms (0.5%)

simplify109.0ms (2.5%)

prune120.0ms (2.7%)

localize7.0ms (0.2%)

series64.0ms (1.5%)

rewrite52.0ms (1.2%)

simplify118.0ms (2.7%)

prune205.0ms (4.7%)

localize10.0ms (0.2%)

series556.0ms (12.6%)

rewrite1.0ms (0%)

simplify37.0ms (0.8%)

prune189.0ms (4.3%)

regimes314.0ms (7.1%)

simplify2.0ms (0%)

end55.0ms (1.3%)

Profiling