Details

analyze345.0ms (14.4%)

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)

sample26.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify141.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

952×	`unsub-neg_binary64`
743×	`sub-neg_binary64`
539×	`distribute-rgt-out_binary64`
467×	`+-commutative_binary64`
464×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	38
1	25	33
2	55	33
3	116	20
4	263	20
5	631	20
6	1195	20
7	2783	20
8	3808	20
9	4029	20
10	4107	20
11	4146	20
12	4222	20
13	4648	20
14	4915	20

prune3.0ms (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

0.1b

Counts

2 → 2

Alt Table

Status	Error	Program
	8.2b	(+.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))
▶	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))

Compiler

Compiled 81 to 49 computations (39.5% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 x.re (.f64 (*.f64 x.re x.im) 3))
0.2b	(.f64 (.f64 x.re x.im) 3)

rewrite40.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 39

Calls

2 calls:

5.0ms	(.f64 x.re (.f64 (*.f64 x.re x.im) 3))
5.0ms	(.f64 (.f64 x.re x.im) 3)

Compiler

Compiled 583 to 331 computations (43.2% saved)

series28.0ms (1.2%)

Error

0.1b

Counts

2 → 12

Calls

2 calls:

14.0ms	(.f64 x.re (.f64 (*.f64 x.re x.im) 3))
11.0ms	(.f64 (.f64 x.re x.im) 3)

Compiler

Compiled 336 to 245 computations (27.1% saved)

simplify87.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

460×	`unswap-sqr_binary64`
419×	`associate-*l/_binary64`
390×	`*-commutative_binary64`
320×	`log-div_binary64`
317×	`associate-/l*_binary64`

Counts

51 → 37

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	741
1	159	608
2	622	608
3	985	605
4	1443	605
5	2625	605
6	4793	605
7	5136	605

prune23.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	33	6	39

Error

0.0b

Counts

39 → 6

Alt Table

Status	Error	Program
	8.2b	(+.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))
	35.2b	(-.f64 (.f64 (sqrt.f64 x.re) (.f64 (*.f64 3 x.im) (pow.f64 x.re 3/2))) (pow.f64 x.im 3))
	0.5b	(-.f64 (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (.f64 3 (*.f64 x.re x.im)) (cbrt.f64 x.re))) (pow.f64 x.im 3))
▶	0.2b	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))
	12.5b	(-.f64 (.f64 x.re (cbrt.f64 (pow.f64 (.f64 3 (*.f64 x.re x.im)) 3))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))

Compiler

Compiled 478 to 321 computations (32.8% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 x.re (.f64 x.re (*.f64 3 x.im)))
0.2b	(.f64 x.re (.f64 3 x.im))

rewrite41.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 39

Calls

2 calls:

6.0ms	(.f64 x.re (.f64 x.re (*.f64 3 x.im)))
4.0ms	(.f64 x.re (.f64 3 x.im))

Compiler

Compiled 570 to 354 computations (37.9% saved)

series28.0ms (1.2%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

14.0ms	(.f64 x.re (.f64 x.re (*.f64 3 x.im)))
13.0ms	(.f64 x.re (.f64 3 x.im))

Compiler

Compiled 336 to 245 computations (27.1% saved)

simplify79.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

465×	`associate-*r/_binary64`
441×	`associate-*l/_binary64`
338×	`*-commutative_binary64`
338×	`associate-+l+_binary64`
307×	`log-div_binary64`

Counts

51 → 39

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	735
1	149	602
2	539	602
3	787	599
4	1128	599
5	1891	599
6	4966	599
7	5323	599

prune28.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	37	8	45

Error

0.0b

Counts

45 → 8

Alt Table

Status	Error	Program
	8.2b	(+.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))
	0.5b	(-.f64 (.f64 x.re (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (*.f64 3 x.im) (cbrt.f64 x.re)))) (pow.f64 x.im 3))
	35.2b	(-.f64 (.f64 (sqrt.f64 x.re) (.f64 (*.f64 3 x.im) (pow.f64 x.re 3/2))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))
	12.5b	(-.f64 (.f64 x.re (cbrt.f64 (pow.f64 (.f64 3 (*.f64 x.re x.im)) 3))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
	0.5b	(-.f64 (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 x.re (.f64 (*.f64 3 x.im) (cbrt.f64 x.re)))) (pow.f64 x.im 3))
▶	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 3 x.re) x.im)) (pow.f64 x.im 3))

Compiler

Compiled 566 to 373 computations (34.1% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 x.re (.f64 (*.f64 3 x.re) x.im))
0.2b	(.f64 (.f64 3 x.re) x.im)

rewrite57.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 39

Calls

2 calls:

7.0ms	(.f64 x.re (.f64 (*.f64 3 x.re) x.im))
4.0ms	(.f64 (.f64 3 x.re) x.im)

Compiler

Compiled 583 to 367 computations (37% saved)

series24.0ms (1%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

13.0ms	(.f64 x.re (.f64 (*.f64 3 x.re) x.im))
10.0ms	(.f64 (.f64 3 x.re) x.im)

Compiler

Compiled 336 to 245 computations (27.1% saved)

simplify85.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

391×	`*-commutative_binary64`
341×	`associate-*r/_binary64`
304×	`log-div_binary64`
302×	`associate-*l/_binary64`
268×	`associate-/l*_binary64`

Counts

51 → 36

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	756
1	161	608
2	625	608
3	921	605
4	1305	605
5	2124	605
6	4445	605
7	4952	605

prune22.0ms (0.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	35	9	44

Error

0.0b

Counts

44 → 9

Alt Table

Status	Error	Program
	8.2b	(+.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))
	0.5b	(-.f64 (.f64 x.re (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (*.f64 3 x.im) (cbrt.f64 x.re)))) (pow.f64 x.im 3))
▶	0.5b	(-.f64 (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 x.re (.f64 (*.f64 3 x.im) (cbrt.f64 x.re)))) (pow.f64 x.im 3))
	8.1b	(-.f64 (.f64 (.f64 3 (pow.f64 x.re 2)) x.im) (pow.f64 x.im 3))
	35.2b	(-.f64 (.f64 (sqrt.f64 x.re) (.f64 (*.f64 3 x.im) (pow.f64 x.re 3/2))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))
	12.5b	(-.f64 (.f64 x.re (cbrt.f64 (pow.f64 (.f64 3 (*.f64 x.re x.im)) 3))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 3 x.re) x.im)) (pow.f64 x.im 3))

Compiler

Compiled 533 to 359 computations (32.6% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
0.6b	(cbrt.f64 x.re)
0.6b	(cbrt.f64 x.re)
0.6b	(cbrt.f64 x.re)

rewrite90.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 73

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
1.0ms	(cbrt.f64 x.re)
1.0ms	(cbrt.f64 x.re)
1.0ms	(cbrt.f64 x.re)

Compiler

Compiled 1557 to 696 computations (55.3% saved)

series59.0ms (2.5%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

15.0ms	(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
13.0ms	(cbrt.f64 x.re)
12.0ms	(cbrt.f64 x.re)
12.0ms	(cbrt.f64 x.re)

Compiler

Compiled 710 to 494 computations (30.4% saved)

simplify97.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

735×	`log-prod_binary64`
577×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
287×	`associate-l_binary64`

Counts

85 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	55	746
1	95	687
2	293	665
3	764	649
4	1760	507
5	4281	507
6	4544	507
7	4811	507

prune35.0ms (1.5%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	65	10	75

Error

0.0b

Counts

75 → 10

Alt Table

Status	Error	Program
	8.2b	(+.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))
	0.5b	(-.f64 (.f64 x.re (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (*.f64 3 x.im) (cbrt.f64 x.re)))) (pow.f64 x.im 3))
	33.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 x.re)) (sqrt.f64 x.re)) (.f64 x.re (.f64 (*.f64 3 x.im) (cbrt.f64 x.re)))) (pow.f64 x.im 3))
	0.5b	(-.f64 (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 x.re (.f64 (*.f64 3 x.im) (cbrt.f64 x.re)))) (pow.f64 x.im 3))
	8.1b	(-.f64 (.f64 (.f64 3 (pow.f64 x.re 2)) x.im) (pow.f64 x.im 3))
	35.2b	(-.f64 (.f64 (sqrt.f64 x.re) (.f64 (*.f64 3 x.im) (pow.f64 x.re 3/2))) (pow.f64 x.im 3))
	0.2b	(-.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) (pow.f64 x.im 3))
	12.5b	(-.f64 (.f64 x.re (cbrt.f64 (pow.f64 (.f64 3 (*.f64 x.re x.im)) 3))) (pow.f64 x.im 3))
	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 x.re x.im) 3)) (pow.f64 x.im 3))
	0.2b	(-.f64 (.f64 x.re (.f64 (*.f64 3 x.re) x.im)) (pow.f64 x.im 3))

Compiler

Compiled 805 to 478 computations (40.6% saved)

regimes151.0ms (6.3%)

Accuracy

Total 0.2b remaining (89.8%)

Threshold costs 0.2b (89.8%)

Compiler

Compiled 2772 to 1848 computations (33.3% saved)

simplify4.0ms (0.2%)

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)

sample860.0ms (36%)

Algorithm

1×

intervals

Results

470.0ms	8000×	body	128	valid
29.0ms	544×	body	128	invalid

Compiler

Compiled 203 to 133 computations (34.5% saved)

Details

analyze345.0ms (14.4%)

sample26.0ms (1.1%)

simplify141.0ms (5.9%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

rewrite40.0ms (1.7%)

series28.0ms (1.2%)

simplify87.0ms (3.6%)

prune23.0ms (1%)

localize7.0ms (0.3%)

rewrite41.0ms (1.7%)

series28.0ms (1.2%)

simplify79.0ms (3.3%)

prune28.0ms (1.2%)

localize10.0ms (0.4%)

rewrite57.0ms (2.4%)

series24.0ms (1%)

simplify85.0ms (3.5%)

prune22.0ms (0.9%)

localize12.0ms (0.5%)

rewrite90.0ms (3.8%)

series59.0ms (2.5%)

simplify97.0ms (4.1%)

prune35.0ms (1.5%)

regimes151.0ms (6.3%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample860.0ms (36%)

Profiling