Details

analyze274.0ms (9.6%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
31.2%	50%	18.8%	7
34.3%	43.7%	22%	8
45.3%	26.5%	28.2%	9
46.8%	23.4%	29.8%	10
48.8%	14%	37.2%	11
49.8%	12.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	6.1%	40.6%	14

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample25.0ms (0.9%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify139.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

613×	`sub-neg_binary64`
578×	`fma-neg_binary64`
529×	`neg-mul-1_binary64`
501×	`neg-sub0_binary64`
455×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	28	31
2	62	31
3	132	20
4	337	20
5	883	20
6	1498	20
7	3513	20
8	4063	20
9	3979	20
10	4616	20
11	4773	20
12	4920	20
13	4916	20

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
	5.9b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 100 to 57 computations (43% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
✓	0.2b	(.f64 x.re (.f64 (*.f64 x.re x.im) 3))
✓	0.3b	(.f64 (.f64 x.re x.im) 3)

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
12×	`cancel-sign-sub-inv_binary64`
12×	`prod-diff_binary64`

Counts

3 → 81

Calls

3 calls:

9.0ms	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
5.0ms	(.f64 x.re (.f64 (*.f64 x.re x.im) 3))
4.0ms	(.f64 (.f64 x.re x.im) 3)

series93.0ms (3.3%)

Counts

3 → 72

Calls

3 calls:

37.0ms	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
33.0ms	(.f64 x.re (.f64 (*.f64 x.re x.im) 3))
23.0ms	(.f64 (.f64 x.re x.im) 3)

simplify150.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

570×	`times-frac_binary64`
446×	`fma-def_binary64`
439×	`fma-neg_binary64`
428×	`exp-prod_binary64`
302×	`cube-prod_binary64`

Counts

153 → 270

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	158	2370
1	307	2210
2	1356	2117
3	3434	2098
4	4442	2095
5	5590	2095

prune116.0ms (4.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	265	5	270
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	267	5	272

Error

0.0b

Counts

272 → 5

Alt Table

Status	Error	Program
	0.3b	(-.f64 (.f64 x.re (.f64 (.f64 (.f64 x.re x.im) (sqrt.f64 3)) (sqrt.f64 3))) (pow.f64 x.im 3))
	0.2b	(-.f64 (.f64 (.f64 (*.f64 x.re x.im) 3) x.re) (pow.f64 x.im 3))
	5.9b	(-.f64 (.f64 (.f64 x.im (pow.f64 x.re 2)) 3) (pow.f64 x.im 3))
▶	0.2b	(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) 3) (pow.f64 x.im 3))
	35.5b	(-.f64 (.f64 (sqrt.f64 x.re) (.f64 (pow.f64 x.re 3/2) (*.f64 3 x.im))) (pow.f64 x.im 3))

Compiler

Compiled 2134 to 1346 computations (36.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) 3) (pow.f64 x.im 3))
✓	0.1b	(.f64 x.re (.f64 x.re x.im))
✓	0.2b	(.f64 (.f64 x.re (*.f64 x.re x.im)) 3)

rewrite24.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
12×	`cancel-sign-sub-inv_binary64`
12×	`prod-diff_binary64`

Counts

3 → 81

Calls

3 calls:

8.0ms	(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) 3) (pow.f64 x.im 3))
7.0ms	(.f64 x.re (.f64 x.re x.im))
5.0ms	(.f64 (.f64 x.re (*.f64 x.re x.im)) 3)

series97.0ms (3.4%)

Counts

3 → 72

Calls

3 calls:

37.0ms	(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) 3) (pow.f64 x.im 3))
34.0ms	(.f64 (.f64 x.re (*.f64 x.re x.im)) 3)
27.0ms	(.f64 x.re (.f64 x.re x.im))

simplify140.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

706×	`fma-neg_binary64`
548×	`*-commutative_binary64`
454×	`fma-def_binary64`
362×	`exp-prod_binary64`
268×	`unswap-sqr_binary64`

Counts

153 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	2380
1	299	2204
2	1301	2103
3	3234	2089
4	4697	2089
5	4612	2089

prune97.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	227	5	232

Error

0.0b

Counts

232 → 5

Alt Table

Status	Error	Program
	0.6b	(-.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 x.re (.f64 x.re x.im))) (cbrt.f64 (.f64 x.re (.f64 x.re x.im)))) (cbrt.f64 (.f64 x.re (*.f64 x.re x.im)))) 3) (pow.f64 x.im 3))
	0.3b	(-.f64 (.f64 x.re (.f64 (.f64 (.f64 x.re x.im) (sqrt.f64 3)) (sqrt.f64 3))) (pow.f64 x.im 3))
▶	0.2b	(-.f64 (.f64 (.f64 (*.f64 x.re x.im) 3) x.re) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) 3) (pow.f64 x.im 3))
	35.5b	(-.f64 (.f64 (sqrt.f64 x.re) (.f64 (pow.f64 x.re 3/2) (*.f64 3 x.im))) (pow.f64 x.im 3))

Compiler

Compiled 2151 to 1255 computations (41.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 (*.f64 x.re x.im) 3) x.re) (pow.f64 x.im 3))
✓	0.2b	(.f64 (.f64 (*.f64 x.re x.im) 3) x.re)
	0.3b	(.f64 (.f64 x.re x.im) 3)

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cancel-sign-sub-inv_binary64`
12×	`prod-diff_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`

Counts

2 → 61

Calls

2 calls:

8.0ms	(-.f64 (.f64 (.f64 (*.f64 x.re x.im) 3) x.re) (pow.f64 x.im 3))
6.0ms	(.f64 (.f64 (*.f64 x.re x.im) 3) x.re)

series69.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

35.0ms	(-.f64 (.f64 (.f64 (*.f64 x.re x.im) 3) x.re) (pow.f64 x.im 3))
34.0ms	(.f64 (.f64 (*.f64 x.re x.im) 3) x.re)

simplify142.0ms (5%)

Algorithm

1×	egg-herbie

Rules

706×	`fma-neg_binary64`
522×	`*-commutative_binary64`
453×	`exp-prod_binary64`
423×	`fma-def_binary64`
260×	`associate-l_binary64`

Counts

109 → 165

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	146	1923
1	286	1779
2	1217	1685
3	2978	1672
4	4437	1671
5	4966	1671
6	4659	1671

prune99.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	223	6	229

Error

0.0b

Counts

229 → 6

Alt Table

Status	Error	Program
	0.6b	(-.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 x.re (.f64 x.re x.im))) (cbrt.f64 (.f64 x.re (.f64 x.re x.im)))) (cbrt.f64 (.f64 x.re (*.f64 x.re x.im)))) 3) (pow.f64 x.im 3))
	0.3b	(-.f64 (.f64 x.re (.f64 (.f64 (.f64 x.re x.im) (sqrt.f64 3)) (sqrt.f64 3))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 (.f64 (*.f64 x.re x.im) 3) x.re) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) 3) (pow.f64 x.im 3))
	35.5b	(-.f64 (.f64 (sqrt.f64 x.re) (.f64 (pow.f64 x.re 3/2) (*.f64 3 x.im))) (pow.f64 x.im 3))
▶	0.2b	(-.f64 (.f64 (.f64 x.re x.im) (*.f64 3 x.re)) (pow.f64 x.im 3))

Compiler

Compiled 2138 to 1332 computations (37.7% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 x.re x.im) (*.f64 3 x.re)) (pow.f64 x.im 3))
✓	0.3b	(.f64 (.f64 x.re x.im) (*.f64 3 x.re))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
12×	`cancel-sign-sub-inv_binary64`
12×	`prod-diff_binary64`

Counts

2 → 62

Calls

2 calls:

7.0ms	(-.f64 (.f64 (.f64 x.re x.im) (*.f64 3 x.re)) (pow.f64 x.im 3))
5.0ms	(.f64 (.f64 x.re x.im) (*.f64 3 x.re))

series72.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(.f64 (.f64 x.re x.im) (*.f64 3 x.re))
35.0ms	(-.f64 (.f64 (.f64 x.re x.im) (*.f64 3 x.re)) (pow.f64 x.im 3))

simplify143.0ms (5%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-neg_binary64`
493×	`*-commutative_binary64`
451×	`exp-prod_binary64`
435×	`fma-def_binary64`
235×	`associate-l_binary64`

Counts

110 → 168

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1934
1	278	1788
2	1145	1694
3	2914	1687
4	4416	1683
5	4964	1683
6	4665	1683

prune67.0ms (2.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	168	6	174

Error

0.0b

Counts

174 → 6

Alt Table

Status	Error	Program
	0.6b	(-.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 x.re (.f64 x.re x.im))) (cbrt.f64 (.f64 x.re (.f64 x.re x.im)))) (cbrt.f64 (.f64 x.re (*.f64 x.re x.im)))) 3) (pow.f64 x.im 3))
	0.3b	(-.f64 (.f64 x.re (.f64 (.f64 (.f64 x.re x.im) (sqrt.f64 3)) (sqrt.f64 3))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 (.f64 (*.f64 x.re x.im) 3) x.re) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) 3) (pow.f64 x.im 3))
	35.5b	(-.f64 (.f64 (sqrt.f64 x.re) (.f64 (pow.f64 x.re 3/2) (*.f64 3 x.im))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 (.f64 x.re x.im) (*.f64 3 x.re)) (pow.f64 x.im 3))

Compiler

Compiled 1624 to 1028 computations (36.7% saved)

regimes180.0ms (6.3%)

Accuracy

Total 0.2b remaining (86.6%)

Threshold costs 0.2b (86.6%)

Compiler

Compiled 3036 to 2097 computations (30.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	16	20
2	21	20
3	23	20
4	24	20
5	24	20

end1.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample828.0ms (29.1%)

Algorithm

1×

intervals

Results

467.0ms	8000×	body	128	valid
33.0ms	568×	body	128	invalid

Compiler

Compiled 137 to 87 computations (36.5% saved)

Details

analyze274.0ms (9.6%)

sample25.0ms (0.9%)

simplify139.0ms (4.9%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

rewrite22.0ms (0.8%)

series93.0ms (3.3%)

simplify150.0ms (5.3%)

prune116.0ms (4.1%)

localize6.0ms (0.2%)

rewrite24.0ms (0.9%)

series97.0ms (3.4%)

simplify140.0ms (4.9%)

prune97.0ms (3.4%)

localize6.0ms (0.2%)

rewrite17.0ms (0.6%)

series69.0ms (2.4%)

simplify142.0ms (5%)

prune99.0ms (3.5%)

localize7.0ms (0.3%)

rewrite16.0ms (0.6%)

series72.0ms (2.5%)

simplify143.0ms (5%)

prune67.0ms (2.4%)

regimes180.0ms (6.3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample828.0ms (29.1%)

Profiling