Details

analyze338.0ms (9.7%)

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%	62.4%	12.6%	6
31.2%	50%	18.8%	7
40.6%	37.5%	22%	8
45.3%	26.5%	28.2%	9
46.8%	19.5%	33.7%	10
48.8%	14%	37.2%	11
51.7%	10.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	5.1%	41.6%	14

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify136.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

686×	`unsub-neg_binary64`
584×	`sub-neg_binary64`
484×	`distribute-rgt-neg-in_binary64`
430×	`distribute-neg-in_binary64`
428×	`distribute-lft-neg-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	38
1	29	33
2	68	33
3	177	20
4	468	20
5	1288	20
6	2217	20
7	3201	20
8	3667	20
9	3742	20
10	3828	20
11	3959	20
12	4290	20
13	4956	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

6.3b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	6.4b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
	6.4b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))

Compiler

Compiled 81 to 49 computations (39.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 (.f64 x.im x.im) -3)
7.0b	(.f64 x.re (.f64 (*.f64 x.im x.im) -3))

rewrite42.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

6.3b

Rules

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

Counts

2 → 40

Calls

2 calls:

6.0ms	(.f64 x.re (.f64 (*.f64 x.im x.im) -3))
5.0ms	(.f64 (.f64 x.im x.im) -3)

Compiler

Compiled 598 to 341 computations (43% saved)

series20.0ms (0.6%)

Error

6.3b

Counts

2 → 9

Calls

2 calls:

13.0ms	(.f64 x.re (.f64 (*.f64 x.im x.im) -3))
5.0ms	(.f64 (.f64 x.im x.im) -3)

Compiler

Compiled 258 to 198 computations (23.3% saved)

simplify78.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

327×	`associate-*r/_binary64`
309×	`*-commutative_binary64`
291×	`associate-*l/_binary64`
252×	`cube-div_binary64`
252×	`log-div_binary64`

Counts

49 → 33

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	703
1	145	573
2	523	564
3	842	564
4	1212	564
5	1991	564
6	4166	564
7	5140	564

prune27.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	30	5	35

Error

6.3b

Counts

35 → 5

Alt Table

Status	Error	Program
	20.2b	(+.f64 (pow.f64 x.re 3) (.f64 (sqrt.f64 (.f64 -3 (.f64 x.re (pow.f64 x.im 2)))) (sqrt.f64 (.f64 -3 (*.f64 x.re (pow.f64 x.im 2))))))
	6.4b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (.f64 (pow.f64 x.im 2) (.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))
▶	6.4b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 x.im (*.f64 -3 x.im))))
✓	6.4b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
	6.4b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))

Compiler

Compiled 481 to 357 computations (25.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 x.im (.f64 -3 x.im))
7.0b	(.f64 x.re (.f64 x.im (*.f64 -3 x.im)))

rewrite42.0ms (1.2%)

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

Compiler

Compiled 570 to 358 computations (37.2% saved)

series29.0ms (0.8%)

Error

6.3b

Counts

2 → 9

Calls

2 calls:

22.0ms	(.f64 x.re (.f64 x.im (*.f64 -3 x.im)))
5.0ms	(.f64 x.im (.f64 -3 x.im))

Compiler

Compiled 258 to 198 computations (23.3% saved)

simplify60.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

557×	`associate-*r/_binary64`
534×	`associate-*l/_binary64`
340×	`associate-+l+_binary64`
302×	`*-commutative_binary64`
248×	`associate-/l/_binary64`

Counts

48 → 32

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	714
1	145	556
2	465	547
3	698	544
4	1000	544
5	1630	544
6	4910	544

prune20.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	32	5	37

Error

6.3b

Counts

37 → 5

Alt Table

Status	Error	Program
	20.2b	(+.f64 (pow.f64 x.re 3) (.f64 (sqrt.f64 (.f64 -3 (.f64 x.re (pow.f64 x.im 2)))) (sqrt.f64 (.f64 -3 (*.f64 x.re (pow.f64 x.im 2))))))
✓	6.4b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 x.im (*.f64 -3 x.im))))
	6.7b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (.f64 (*.f64 -3 x.im) (cbrt.f64 x.im)))))
✓	6.4b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
▶	6.4b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))

Compiler

Compiled 458 to 325 computations (29% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x.re x.re) (.f64 x.im x.im))
0.1b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
6.0b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

rewrite78.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`associate-*l/_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 70

Calls

4 calls:

7.0ms	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
5.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
5.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
3.0ms	(-.f64 (.f64 x.re x.re) (.f64 x.im x.im))

Compiler

Compiled 2262 to 306 computations (86.5% saved)

series89.0ms (2.6%)

Error

5.0b

Counts

4 → 42

Calls

4 calls:

24.0ms	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
22.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
17.0ms	(-.f64 (.f64 x.re x.re) (.f64 x.im x.im))
14.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)

Compiler

Compiled 1280 to 802 computations (37.3% saved)

simplify106.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

557×	`cancel-sign-sub-inv_binary64`
331×	`unswap-sqr_binary64`
221×	`associate-l_binary64`
195×	`associate-r_binary64`
185×	`distribute-rgt-out_binary64`

Counts

112 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	2723
1	422	2177
2	1572	2106
3	3023	2092
4	4985	2092

prune60.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	74	5	79

Error

0.0b

Counts

79 → 5

Alt Table

Status	Error	Program
	20.2b	(+.f64 (pow.f64 x.re 3) (.f64 (sqrt.f64 (.f64 -3 (.f64 x.re (pow.f64 x.im 2)))) (sqrt.f64 (.f64 -3 (*.f64 x.re (pow.f64 x.im 2))))))
✓	6.4b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 x.im (*.f64 -3 x.im))))
▶	0.2b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
✓	6.4b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
	6.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (pow.f64 x.re 3) (.f64 x.re (pow.f64 x.im 2)))) (cbrt.f64 (-.f64 (pow.f64 x.re 3) (.f64 x.re (pow.f64 x.im 2))))) (cbrt.f64 (-.f64 (pow.f64 x.re 3) (.f64 x.re (pow.f64 x.im 2))))) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))

Compiler

Compiled 1673 to 865 computations (48.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x.re (-.f64 x.re x.im))
0.1b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.2b	(.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im)))

rewrite302.0ms (8.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

36×	`distribute-lft-in_binary64`
36×	`distribute-rgt-in_binary64`
31×	`cancel-sign-sub-inv_binary64`
26×	`associate-*r/_binary64`
25×	`add-sqr-sqrt_binary64`

Counts

4 → 137

Calls

4 calls:

12.0ms	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
11.0ms	(.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im)))
5.0ms	(*.f64 x.re (-.f64 x.re x.im))
5.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)

Compiler

Compiled 4717 to 706 computations (85% saved)

series84.0ms (2.4%)

Error

0.0b

Counts

4 → 42

Calls

4 calls:

24.0ms	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
24.0ms	(.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im)))
15.0ms	(*.f64 x.re (-.f64 x.re x.im))
13.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)

Compiler

Compiled 1322 to 786 computations (40.5% saved)

simplify300.0ms (8.6%)

Algorithm

1×	egg-herbie

Rules

668×	`associate-l_binary64`
624×	`associate-r_binary64`
315×	`distribute-rgt-in_binary64`
300×	`distribute-lft-in_binary64`
294×	`cancel-sign-sub-inv_binary64`

Counts

179 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	5562
1	872	4250
2	3700	4129
3	4243	4129
4	4716	4129

prune123.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	2	0	2
Picked	1	0	1
Done	0	2	2
Total	137	7	144

Error

Counts

144 → 7

Alt Table

Status	Error	Program
	2.4b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x.re x.im)) (cbrt.f64 (+.f64 x.re x.im))) (.f64 x.re (.f64 (-.f64 x.re x.im) (cbrt.f64 (+.f64 x.re x.im))))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
	6.4b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
	0.7b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (-.f64 x.re x.im) (cbrt.f64 x.re)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
	0.2b	(+.f64 (.f64 (.f64 x.re x.re) (+.f64 x.re x.im)) (.f64 (neg.f64 x.im) (+.f64 (.f64 x.re (+.f64 x.re x.im)) (.f64 2 (.f64 x.re x.im)))))
	6.4b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 x.im (*.f64 -3 x.im))))
	21.2b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (sqrt.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))) (sqrt.f64 (.f64 x.im (.f64 2 (*.f64 x.re x.im))))))
	0.5b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 x.re (-.f64 x.re x.im))) (.f64 (.f64 (cbrt.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))) (cbrt.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im))))) (cbrt.f64 (.f64 x.im (.f64 2 (*.f64 x.re x.im))))))

Compiler

Compiled 2209 to 992 computations (55.1% saved)

regimes541.0ms (15.5%)

Accuracy

Total 0.1b remaining (87.5%)

Threshold costs 0.1b (87.5%)

Compiler

Compiled 10783 to 5948 computations (44.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	16	20
2	16	20

end1.0ms (0%)

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

sample940.0ms (26.9%)

Algorithm

1×

intervals

Results

571.0ms	8000×	body	128	valid
30.0ms	483×	body	128	invalid

Compiler

Compiled 214 to 121 computations (43.5% saved)

Details

analyze338.0ms (9.7%)

sample26.0ms (0.7%)

simplify136.0ms (3.9%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite42.0ms (1.2%)

series20.0ms (0.6%)

simplify78.0ms (2.2%)

prune27.0ms (0.8%)

localize7.0ms (0.2%)

rewrite42.0ms (1.2%)

series29.0ms (0.8%)

simplify60.0ms (1.7%)

prune20.0ms (0.6%)

localize14.0ms (0.4%)

rewrite78.0ms (2.2%)

series89.0ms (2.6%)

simplify106.0ms (3.1%)

prune60.0ms (1.7%)

localize11.0ms (0.3%)

rewrite302.0ms (8.7%)

series84.0ms (2.4%)

simplify300.0ms (8.6%)

prune123.0ms (3.5%)

regimes541.0ms (15.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample940.0ms (26.9%)

Profiling