Details

analyze305.0ms (11.2%)

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)

sample21.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify152.0ms (5.6%)

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

prune5.0ms (0.2%)

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

9.9b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	9.9b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
	10.0b	(-.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)

localize11.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 (.f64 x.im x.im) -3)
9.8b	(.f64 x.re (.f64 (*.f64 x.im x.im) -3))

rewrite64.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

9.8b

Rules

16×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-l_binary64` `associate-r*_binary64`
2×	`add-log-exp_binary64` `*-commutative_binary64`

Counts

2 → 40

Calls

2 calls:

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

Compiler

Compiled 598 to 341 computations (43% saved)

series29.0ms (1.1%)

Error

9.9b

Counts

2 → 9

Calls

2 calls:

19.0ms	(.f64 x.re (.f64 (*.f64 x.im x.im) -3))
8.0ms	(.f64 (.f64 x.im x.im) -3)

Compiler

Compiled 258 to 198 computations (23.3% saved)

simplify84.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

318×	`associate-*r/_binary64`
296×	`*-commutative_binary64`
283×	`associate-*l/_binary64`
252×	`log-div_binary64` `cube-div_binary64`
234×	`unswap-sqr_binary64`

Counts

49 → 33

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	703
1	143	573
2	504	564
3	799	564
4	1140	564
5	1884	564
6	3974	564
7	4948	564

prune44.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	27	6	33
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	28	7	35

Error

9.8b

Counts

35 → 7

Alt Table

Status	Error	Program
	37.5b	(+.f64 (pow.f64 x.re 3) (.f64 (sqrt.f64 x.re) (.f64 (*.f64 -3 (pow.f64 x.im 2)) (sqrt.f64 x.re))))
▶	9.9b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 x.im 2) x.re) -3))
	25.9b	(+.f64 (pow.f64 x.re 3) (.f64 (sqrt.f64 (.f64 -3 (.f64 (pow.f64 x.im 2) x.re))) (sqrt.f64 (.f64 -3 (*.f64 (pow.f64 x.im 2) x.re)))))
	10.2b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (.f64 -3 (pow.f64 x.im 2)) (cbrt.f64 x.re))))
✓	9.9b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
	10.2b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (cbrt.f64 (.f64 -3 (.f64 (pow.f64 x.im 2) x.re))) (cbrt.f64 (.f64 -3 (.f64 (pow.f64 x.im 2) x.re)))) (cbrt.f64 (.f64 -3 (.f64 (pow.f64 x.im 2) x.re)))))
	9.9b	(+.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))))

Compiler

Compiled 577 to 437 computations (24.3% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 (.f64 (pow.f64 x.im 2) x.re) -3)
9.8b	(*.f64 (pow.f64 x.im 2) x.re)

rewrite91.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

17×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`prod-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-l_binary64`
6×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`

Counts

2 → 46

Calls

2 calls:

6.0ms	(.f64 (.f64 (pow.f64 x.im 2) x.re) -3)
6.0ms	(*.f64 (pow.f64 x.im 2) x.re)

Compiler

Compiled 732 to 532 computations (27.3% saved)

series36.0ms (1.3%)

Error

9.8b

Counts

2 → 12

Calls

2 calls:

18.0ms	(.f64 (.f64 (pow.f64 x.im 2) x.re) -3)
16.0ms	(*.f64 (pow.f64 x.im 2) x.re)

Compiler

Compiled 336 to 258 computations (23.2% saved)

simplify133.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

387×	`unswap-sqr_binary64`
357×	`distribute-rgt-in_binary64`
339×	`associate-/l*_binary64`
321×	`distribute-lft-in_binary64`
258×	`*-commutative_binary64`

Counts

58 → 31

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	78	812
1	155	683
2	505	683
3	801	683
4	1194	683
5	2286	683
6	4358	683
7	4989	683
8	4992	683
9	4983	683

prune40.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	28	10	38

Error

0.1b

Counts

38 → 10

Alt Table

Status	Error	Program
	37.5b	(+.f64 (pow.f64 x.re 3) (.f64 (sqrt.f64 x.re) (.f64 (*.f64 -3 (pow.f64 x.im 2)) (sqrt.f64 x.re))))
✓	9.9b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 x.im 2) x.re) -3))
	25.9b	(+.f64 (pow.f64 x.re 3) (.f64 (sqrt.f64 (.f64 -3 (.f64 (pow.f64 x.im 2) x.re))) (sqrt.f64 (.f64 -3 (*.f64 (pow.f64 x.im 2) x.re)))))
	10.2b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (.f64 -3 (pow.f64 x.im 2)) (cbrt.f64 x.re))))
✓	9.9b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
	34.3b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 x.im (*.f64 x.re (pow.f64 (sqrt.f64 x.im) 2))) -3))
	10.2b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (cbrt.f64 (.f64 -3 (.f64 (pow.f64 x.im 2) x.re))) (cbrt.f64 (.f64 -3 (.f64 (pow.f64 x.im 2) x.re)))) (cbrt.f64 (.f64 -3 (.f64 (pow.f64 x.im 2) x.re)))))
	3.9b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) 2) (.f64 x.re (pow.f64 (cbrt.f64 x.im) 2))) -3))
	9.9b	(+.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))))
▶	0.2b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re)) -3))

Compiler

Compiled 575 to 419 computations (27.1% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 (pow.f64 x.im (/.f64 2 2)) (.f64 x.im x.re))
0.2b	(.f64 (.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re)) -3)

rewrite89.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

36×	`add-exp-log_binary64`
25×	`prod-exp_binary64`
16×	`add-cbrt-cube_binary64`
9×	`cbrt-unprod_binary64`
8×	`associate-l_binary64`

Counts

2 → 47

Calls

2 calls:

8.0ms	(.f64 (.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re)) -3)
6.0ms	(.f64 (pow.f64 x.im (/.f64 2 2)) (.f64 x.im x.re))

Compiler

Compiled 978 to 672 computations (31.3% saved)

series37.0ms (1.3%)

Error

0.1b

Counts

2 → 12

Calls

2 calls:

19.0ms	(.f64 (.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re)) -3)
16.0ms	(.f64 (pow.f64 x.im (/.f64 2 2)) (.f64 x.im x.re))

Compiler

Compiled 336 to 258 computations (23.2% saved)

simplify107.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

501×	`distribute-rgt-in_binary64`
448×	`distribute-lft-in_binary64`
419×	`*-commutative_binary64`
391×	`sqr-pow_binary64`
199×	`times-frac_binary64`

Counts

59 → 41

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	86	856
1	169	702
2	682	702
3	1238	702
4	1786	702
5	2854	702
6	4904	702
7	4868	702

prune43.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	5	2	7
Picked	0	1	1
Done	0	2	2
Total	43	8	51

Error

0.0b

Counts

51 → 8

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (pow.f64 x.re 3) (.f64 (pow.f64 x.im (/.f64 2 2)) (.f64 -3 (*.f64 x.im x.re))))
✓	9.9b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 x.im 2) x.re) -3))
	10.2b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (.f64 -3 (pow.f64 x.im 2)) (cbrt.f64 x.re))))
	37.5b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 (sqrt.f64 x.im) (/.f64 2 2)) (*.f64 x.re (pow.f64 x.im 3/2))) -3))
✓	9.9b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
	0.6b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (/.f64 2 2)) (.f64 (*.f64 x.im x.re) (cbrt.f64 x.im))) -3))
	9.9b	(+.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))))
✓	0.2b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re)) -3))

Compiler

Compiled 628 to 471 computations (25% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (pow.f64 x.im (/.f64 2 2)) (.f64 -3 (*.f64 x.im x.re)))
0.3b	(.f64 -3 (.f64 x.im x.re))

rewrite84.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-exp-log_binary64`
21×	`prod-exp_binary64`
16×	`add-cbrt-cube_binary64`
10×	`associate-l_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 46

Calls

2 calls:

9.0ms	(.f64 (pow.f64 x.im (/.f64 2 2)) (.f64 -3 (*.f64 x.im x.re)))
5.0ms	(.f64 -3 (.f64 x.im x.re))

Compiler

Compiled 906 to 623 computations (31.2% saved)

series36.0ms (1.3%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

18.0ms	(.f64 (pow.f64 x.im (/.f64 2 2)) (.f64 -3 (*.f64 x.im x.re)))
16.0ms	(.f64 -3 (.f64 x.im x.re))

Compiler

Compiled 388 to 297 computations (23.5% saved)

simplify91.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-+l+_binary64`
533×	`distribute-rgt-in_binary64`
436×	`*-commutative_binary64`
389×	`associate-+r+_binary64`
383×	`sqr-pow_binary64`

Counts

58 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	83	860
1	165	707
2	592	707
3	1043	707
4	1683	707
5	3413	707
6	4855	707

prune40.0ms (1.5%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	2	2	4
Picked	0	1	1
Done	0	3	3
Total	37	9	46

Error

0.0b

Counts

46 → 9

Alt Table

Status	Error	Program
	0.2b	(+.f64 (pow.f64 x.re 3) (.f64 (pow.f64 x.im (/.f64 2 2)) (.f64 -3 (*.f64 x.im x.re))))
	0.2b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 -3 x.im) (*.f64 x.im x.re)))
	0.6b	(+.f64 (pow.f64 x.re 3) (.f64 (pow.f64 (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (/.f64 2 2)) (.f64 (.f64 -3 (*.f64 x.im x.re)) (cbrt.f64 x.im))))
	9.9b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 x.im 2) x.re) -3))
	10.2b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (.f64 -3 (pow.f64 x.im 2)) (cbrt.f64 x.re))))
	37.5b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 (sqrt.f64 x.im) (/.f64 2 2)) (*.f64 x.re (pow.f64 x.im 3/2))) -3))
	12.7b	(+.f64 (pow.f64 x.re 3) (.f64 (pow.f64 x.im (/.f64 2 2)) (cbrt.f64 (pow.f64 (.f64 -3 (*.f64 x.im x.re)) 3))))
	9.9b	(+.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 (*.f64 x.im x.im) -3)))
	0.2b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 (pow.f64 x.im (/.f64 2 2)) (*.f64 x.im x.re)) -3))

Compiler

Compiled 484 to 350 computations (27.7% saved)

regimes340.0ms (12.5%)

Accuracy

Total 0.2b remaining (91.2%)

Threshold costs 0.2b (91.2%)

Compiler

Compiled 4887 to 3603 computations (26.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`unpow1_binary64` `1-exp_binary64` `+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	20
1	22	20
2	20	20

end1.0ms (0%)

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

sample815.0ms (29.9%)

Algorithm

1×

intervals

Results

366.0ms	8000×	body	128	valid
19.0ms	434×	body	128	invalid

Compiler

Compiled 194 to 138 computations (28.9% saved)

Details

analyze305.0ms (11.2%)

sample21.0ms (0.8%)

simplify152.0ms (5.6%)

prune5.0ms (0.2%)

localize11.0ms (0.4%)

rewrite64.0ms (2.3%)

series29.0ms (1.1%)

simplify84.0ms (3.1%)

prune44.0ms (1.6%)

localize7.0ms (0.3%)

rewrite91.0ms (3.3%)

series36.0ms (1.3%)

simplify133.0ms (4.9%)

prune40.0ms (1.5%)

localize9.0ms (0.3%)

rewrite89.0ms (3.3%)

series37.0ms (1.3%)

simplify107.0ms (3.9%)

prune43.0ms (1.6%)

localize9.0ms (0.3%)

rewrite84.0ms (3.1%)

series36.0ms (1.3%)

simplify91.0ms (3.3%)

prune40.0ms (1.5%)

regimes340.0ms (12.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample815.0ms (29.9%)

Profiling