Details

analyze168.0ms (7.7%)

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)

sample104.0ms (4.7%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	19×	body	128	invalid

Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify129.0ms (5.9%)

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	12	24
1	26	23
2	60	23
3	130	16
4	335	16
5	881	16
6	1496	16
7	3511	16
8	4061	16
9	3977	16
10	4614	16
11	4771	16
12	4918	16
13	4914	16

prune3.0ms (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

6.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.0b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	7.0b	(+.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 54 computations (46% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im)))
✓	6.5b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))

series23.0ms (1%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
9.0ms	(fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im)))

rewrite70.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

3.0ms	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
0.0ms	(fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im)))

simplify106.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

435×	`exp-prod_binary64`
356×	`unswap-sqr_binary64`
355×	`fma-def_binary64`
319×	`*-commutative_binary64`
271×	`associate-l_binary64`

Counts

80 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	1276
1	116	1183
2	336	1183
3	1136	1183
4	2105	1183
5	4465	1183
6	4949	1183
7	4916	1183

prune46.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	6	68

Error

6.6b

Counts

68 → 6

Alt Table

Status	Error	Program
✓	7.0b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	7.0b	(.f64 x.im (-.f64 (.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))
	28.1b	(.f64 (.f64 x.im (sqrt.f64 (fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im))))) (sqrt.f64 (fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im)))))
	33.5b	(neg.f64 (pow.f64 x.im 3))
	7.0b	(+.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))
▶	6.9b	(-.f64 (.f64 3 (.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))

Compiler

Compiled 1270 to 615 computations (51.6% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (.f64 (pow.f64 x.re 2) x.im))
✓	6.8b	(*.f64 (pow.f64 x.re 2) x.im)

series19.0ms (0.9%)

Counts

2 → 0

Calls

2 calls:

11.0ms	(.f64 3 (.f64 (pow.f64 x.re 2) x.im))
8.0ms	(*.f64 (pow.f64 x.re 2) x.im)

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`associate-l_binary64`
10×	`prod-exp_binary64`
9×	`add-cbrt-cube_binary64`

Counts

2 → 50

Calls

2 calls:

4.0ms	(.f64 3 (.f64 (pow.f64 x.re 2) x.im))
4.0ms	(*.f64 (pow.f64 x.re 2) x.im)

simplify66.0ms (3%)

Algorithm

1×	egg-herbie

Rules

495×	`unswap-sqr_binary64`
357×	`distribute-rgt-in_binary64`
321×	`distribute-lft-in_binary64`
310×	`log-prod_binary64`
307×	`fma-def_binary64`

Counts

50 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	77	615
1	150	501
2	451	501
3	737	501
4	1216	501
5	2847	501
6	4638	501
7	4773	501

prune66.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	76	5	81

Error

0.0b

Counts

81 → 5

Alt Table

Status	Error	Program
✓	7.0b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	6.9b	(-.f64 (.f64 3 (.f64 (*.f64 x.re x.re) x.im)) (pow.f64 x.im 3))
	7.0b	(.f64 x.im (-.f64 (.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))
	7.1b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 (pow.f64 x.re 2) x.im))) (pow.f64 x.im 3))
▶	0.2b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))

Compiler

Compiled 1365 to 904 computations (33.8% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))
✓	0.2b	(.f64 x.re (.f64 x.re x.im))

series21.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

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

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

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

simplify92.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

475×	`unswap-sqr_binary64`
366×	`times-frac_binary64`
338×	`associate-+l+_binary64`
333×	`sqr-pow_binary64`
318×	`*-commutative_binary64`

Counts

91 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	965
1	143	848
2	504	848
3	772	846
4	1133	846
5	2151	846
6	3985	846
7	4494	846
8	4862	846

prune51.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	61	6	67

Error

0.0b

Counts

67 → 6

Alt Table

Status	Error	Program
✓	7.0b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	6.9b	(-.f64 (.f64 3 (.f64 (*.f64 x.re x.re) x.im)) (pow.f64 x.im 3))
	7.0b	(.f64 x.im (-.f64 (.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))
✓	0.2b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
▶	0.2b	(-.f64 (.f64 (.f64 3 x.re) (*.f64 x.re x.im)) (pow.f64 x.im 3))
	0.4b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (.f64 x.re (.f64 x.re x.im)))) (pow.f64 x.im 3))

Compiler

Compiled 1149 to 599 computations (47.9% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 3 x.re) (*.f64 x.re x.im))

series11.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

11.0ms

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

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`
8×	`cbrt-unprod_binary64`
8×	`prod-exp_binary64`

Counts

1 → 24

Calls

1 calls:

5.0ms

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

simplify88.0ms (4%)

Algorithm

1×	egg-herbie

Rules

431×	`distribute-rgt-in_binary64`
388×	`distribute-lft-in_binary64`
343×	`associate-+l+_binary64`
323×	`*-commutative_binary64`
312×	`unswap-sqr_binary64`

Counts

48 → 31

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	607
1	122	517
2	473	517
3	709	517
4	1021	517
5	1822	517
6	3315	517
7	4730	517
8	4999	517
9	4890	517

prune25.0ms (1.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	31	6	37

Error

0.0b

Counts

37 → 6

Alt Table

Status	Error	Program
✓	7.0b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	6.9b	(-.f64 (.f64 3 (.f64 (*.f64 x.re x.re) x.im)) (pow.f64 x.im 3))
	7.0b	(.f64 x.im (-.f64 (.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))
✓	0.2b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 (.f64 3 x.re) (*.f64 x.re x.im)) (pow.f64 x.im 3))
	0.4b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (.f64 x.re (.f64 x.re x.im)))) (pow.f64 x.im 3))

Compiler

Compiled 609 to 350 computations (42.5% saved)

regimes109.0ms (5%)

Accuracy

Total 0.2b remaining (88.1%)

Threshold costs 0.2b (88.1%)

Counts

33 → 1

Compiler

Compiled 1857 to 1236 computations (33.4% saved)

simplify3.0ms (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	9	16
1	14	16
2	19	16
3	21	16
4	22	16
5	22	16

end1.0ms (0%)

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

sample946.0ms (43%)

Algorithm

1×

intervals

Results

571.0ms	8000×	body	128	valid
65.0ms	595×	body	128	invalid

Compiler

Compiled 119 to 81 computations (31.9% saved)

Details

analyze168.0ms (7.7%)

sample104.0ms (4.7%)

simplify129.0ms (5.9%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series23.0ms (1%)

rewrite70.0ms (3.2%)

simplify106.0ms (4.8%)

prune46.0ms (2.1%)

localize6.0ms (0.3%)

series19.0ms (0.9%)

rewrite10.0ms (0.5%)

simplify66.0ms (3%)

prune66.0ms (3%)

localize6.0ms (0.3%)

series21.0ms (0.9%)

rewrite11.0ms (0.5%)

simplify92.0ms (4.2%)

prune51.0ms (2.3%)

localize6.0ms (0.3%)

series11.0ms (0.5%)

rewrite6.0ms (0.3%)

simplify88.0ms (4%)

prune25.0ms (1.2%)

regimes109.0ms (5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample946.0ms (43%)

Profiling