Details

analyze190.0ms (6.1%)

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
81.2%	18.7%	0.1%	5
81.2%	15.6%	3.2%	6
81.2%	15.6%	3.2%	7
81.2%	14%	4.8%	8
81.2%	14%	4.8%	9
81.2%	13.3%	5.6%	10
81.2%	13.3%	5.6%	11
81.2%	12.9%	6%	12
81.2%	12.9%	6%	13
81.2%	12.7%	6.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample69.0ms (2.2%)

Algorithm

1×

intervals

Results

33.0ms	32×	body	1024	valid
11.0ms	194×	body	128	valid
7.0ms	24×	body	1024	invalid
4.0ms	23×	body	512	valid
2.0ms	10×	body	512	invalid
1.0ms	18×	body	128	invalid
1.0ms	7×	body	256	valid
0.0ms	3×	body	256	invalid

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify10.0ms (0.3%)

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

prune2.0ms (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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (exp.f64 re) (sin.f64 im))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (exp.f64 re) (sin.f64 im))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

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

series21.0ms (0.7%)

Counts

1 → 8

Calls

1 calls:

21.0ms

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

simplify73.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

963×	`fma-neg_binary64`
601×	`cancel-sign-sub-inv_binary64`
423×	`unswap-sqr_binary64`
355×	`distribute-rgt-neg-in_binary64`
283×	`*-commutative_binary64`

Counts

28 → 48

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	408
1	185	370
2	527	349
3	1418	335
4	2537	333
5	4402	333
6	4955	333

prune29.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	3	49

Error

0.2b

Counts

49 → 3

Alt Table

Status	Error	Program
	23.6b	(.f64 (sin.f64 im) (+.f64 (fma.f64 1/2 (.f64 re re) re) (fma.f64 1/6 (pow.f64 re 3) 1)))
✓	0.3b	(*.f64 (exp.f64 re) (sin.f64 im))
▶	18.5b	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))

Compiler

Compiled 574 to 226 computations (60.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (exp.f64 re) (sin.f64 im))
	0.2b	(*.f64 (exp.f64 re) (sin.f64 im))
	0.3b	(sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im)))
✓	0.3b	(sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im)))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`sqrt-pow1_binary64`
1×	`*-un-lft-identity_binary64`
1×	`sqrt-prod_binary64`
1×	`pow-prod-down_binary64`

Counts

1 → 13

Calls

1 calls:

3.0ms

(sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im)))

series30.0ms (1%)

Counts

1 → 4

Calls

1 calls:

30.0ms

(sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im)))

simplify100.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

741×	`distribute-lft-out_binary64`
481×	`associate-/l/_binary64`
474×	`*-commutative_binary64`
468×	`fma-def_binary64`
415×	`associate-/r/_binary64`

Counts

17 → 29

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	241
1	78	221
2	180	206
3	457	198
4	1161	197
5	1671	197
6	2622	197
7	2603	197
8	3162	197
9	4987	197
10	4905	197

prune61.0ms (1.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	202	3	205

Error

0.2b

Counts

205 → 3

Alt Table

Status	Error	Program
▶	23.6b	(.f64 (sin.f64 im) (+.f64 (fma.f64 1/2 (.f64 re re) re) (fma.f64 1/6 (pow.f64 re 3) 1)))
✓	0.3b	(*.f64 (exp.f64 re) (sin.f64 im))
✓	18.5b	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))

Compiler

Compiled 2719 to 676 computations (75.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (*.f64 re re) re)
✓	0.1b	(fma.f64 1/6 (pow.f64 re 3) 1)
✓	1.7b	(.f64 (sin.f64 im) (+.f64 (fma.f64 1/2 (.f64 re re) re) (fma.f64 1/6 (pow.f64 re 3) 1)))
✓	11.3b	(+.f64 (fma.f64 1/2 (*.f64 re re) re) (fma.f64 1/6 (pow.f64 re 3) 1))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`

Counts

4 → 64

Calls

4 calls:

6.0ms	(.f64 (sin.f64 im) (+.f64 (fma.f64 1/2 (.f64 re re) re) (fma.f64 1/6 (pow.f64 re 3) 1)))
3.0ms	(+.f64 (fma.f64 1/2 (*.f64 re re) re) (fma.f64 1/6 (pow.f64 re 3) 1))
0.0ms	(fma.f64 1/2 (*.f64 re re) re)
0.0ms	(fma.f64 1/6 (pow.f64 re 3) 1)

series68.0ms (2.2%)

Counts

4 → 60

Calls

4 calls:

42.0ms	(.f64 (sin.f64 im) (+.f64 (fma.f64 1/2 (.f64 re re) re) (fma.f64 1/6 (pow.f64 re 3) 1)))
12.0ms	(fma.f64 1/6 (pow.f64 re 3) 1)
9.0ms	(fma.f64 1/2 (*.f64 re re) re)
4.0ms	(+.f64 (fma.f64 1/2 (*.f64 re re) re) (fma.f64 1/6 (pow.f64 re 3) 1))

simplify79.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

776×	`associate-+r+_binary64`
424×	`associate--r+_binary64`
382×	`associate--l+_binary64`
277×	`cancel-sign-sub-inv_binary64`
192×	`fma-def_binary64`

Counts

124 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	2498
1	482	2322
2	1905	2253
3	5083	2253

prune89.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	207	3	210

Error

0.2b

Counts

210 → 3

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (exp.f64 re) (sin.f64 im))
▶	37.8b	(cbrt.f64 (pow.f64 (.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im)) 3))
✓	18.5b	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))

Compiler

Compiled 3200 to 1980 computations (38.1% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im)) 3)
✓	1.7b	(.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im))
✓	11.3b	(fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (*.f64 re re) (+.f64 1 re)))
✓	21.1b	(cbrt.f64 (pow.f64 (.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im)) 3))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`*-un-lft-identity_binary64`

Counts

4 → 73

Calls

4 calls:

3.0ms	(pow.f64 (.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im)) 3)
3.0ms	(.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im))
2.0ms	(cbrt.f64 (pow.f64 (.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im)) 3))
0.0ms	(fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (*.f64 re re) (+.f64 1 re)))

series204.0ms (6.5%)

Counts

4 → 84

Calls

4 calls:

113.0ms	(pow.f64 (.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im)) 3)
45.0ms	(.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im))
42.0ms	(cbrt.f64 (pow.f64 (.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im)) 3))
3.0ms	(fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (*.f64 re re) (+.f64 1 re)))

simplify105.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-def_binary64`
519×	`associate-+r+_binary64`
464×	`associate-r_binary64`
336×	`associate-l_binary64`
305×	`associate-+l+_binary64`

Counts

157 → 294

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	391	5809
1	1142	5122
2	5047	5122

prune165.0ms (5.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	294	3	297

Error

0.2b

Counts

297 → 3

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (exp.f64 re) (sin.f64 im))
✓	37.8b	(cbrt.f64 (pow.f64 (.f64 (fma.f64 1/6 (pow.f64 re 3) (fma.f64 1/2 (.f64 re re) (+.f64 1 re))) (sin.f64 im)) 3))
✓	18.5b	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))

Compiler

Compiled 6974 to 4791 computations (31.3% saved)

regimes131.0ms (4.2%)

Accuracy

Total 0.0b remaining (12.9%)

Threshold costs 0.0b (12.9%)

Compiler

Compiled 1757 to 1175 computations (33.1% saved)

simplify3.0ms (0.1%)

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

end0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample1.6s (52.4%)

Algorithm

1×

intervals

Results

469.0ms	1310×	body	1024	valid
334.0ms	5644×	body	128	valid
187.0ms	629×	body	1024	invalid
121.0ms	702×	body	512	valid
55.0ms	333×	body	512	invalid
48.0ms	808×	body	128	invalid
37.0ms	338×	body	256	valid
18.0ms	172×	body	256	invalid
4.0ms	6×	body	2048	valid

Compiler

Compiled 60 to 41 computations (31.7% saved)

Details

analyze190.0ms (6.1%)

sample69.0ms (2.2%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite5.0ms (0.2%)

series21.0ms (0.7%)

simplify73.0ms (2.3%)

prune29.0ms (0.9%)

localize7.0ms (0.2%)

rewrite3.0ms (0.1%)

series30.0ms (1%)

simplify100.0ms (3.2%)

prune61.0ms (1.9%)

localize11.0ms (0.3%)

rewrite13.0ms (0.4%)

series68.0ms (2.2%)

simplify79.0ms (2.5%)

prune89.0ms (2.8%)

localize14.0ms (0.4%)

rewrite12.0ms (0.4%)

series204.0ms (6.5%)

simplify105.0ms (3.3%)

prune165.0ms (5.3%)

regimes131.0ms (4.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (52.4%)

Profiling