Details

analyze176.0ms (4.8%)

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)

sample1.7s (44.9%)

Results

1.5s	8256×	body	128	valid
69.0ms	411×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify22.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

594×	`fma-neg_binary64`
507×	`fma-def_binary64`
396×	`cancel-sign-sub-inv_binary64`
243×	`associate--l+_binary64`
211×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	31	25
2	78	23
3	241	16
4	745	14
5	2583	14

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

6.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.6b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))
	6.7b	(-.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 97 to 55 computations (43.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x.im (.f64 x.im -3))
✓	6.1b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))

series14.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

12.0ms	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))
2.0ms	(.f64 x.im (.f64 x.im -3))

rewrite43.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

747×	`log1p-expm1-u_binary64`
747×	`expm1-log1p-u_binary64`
176×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	185	21
2	2085	21

Stop Event

1×	node limit

Counts

2 → 39

Calls

2 calls:

43.0ms	(.f64 x.im (.f64 x.im -3))
43.0ms	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

984×	`fma-def_binary64`
593×	`unswap-sqr_binary64`
342×	`fma-neg_binary64`
255×	`distribute-rgt-neg-in_binary64`
232×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	414
1	37	414
2	92	378
3	251	378
4	757	378
5	1495	378
6	2222	378
7	3499	378

Stop Event

1×	node limit

Counts

75 → 46

prune44.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	43	5	48

Error

0.0b

Counts

48 → 5

Alt Table

Status	Error	Program
✓	6.6b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))
	6.7b	(-.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	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
	30.3b	(.f64 (.f64 x.im x.im) (*.f64 -3 x.re))
	7.2b	(pow.f64 (cbrt.f64 (fma.f64 x.re (.f64 -3 (.f64 x.im x.im)) (pow.f64 x.re 3))) 3)

Compiler

Compiled 771 to 475 computations (38.4% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
5.0ms	(.f64 x.im (.f64 -3 x.re))

rewrite41.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

761×	`log1p-expm1-u_binary64`
761×	`expm1-log1p-u_binary64`
164×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	186	21
2	2117	21

Stop Event

1×	node limit

Counts

2 → 38

Calls

2 calls:

40.0ms	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
40.0ms	(.f64 x.im (.f64 -3 x.re))

simplify43.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

989×	`fma-def_binary64`
593×	`unswap-sqr_binary64`
342×	`fma-neg_binary64`
322×	`cancel-sign-sub-inv_binary64`
254×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	498
1	40	498
2	96	462
3	248	462
4	723	462
5	1466	462
6	2182	462
7	3412	462

Stop Event

1×	node limit

Counts

86 → 45

prune45.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	43	7	50

Error

0.0b

Counts

50 → 7

Alt Table

Status	Error	Program
✓	6.6b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))
	6.7b	(-.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	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
	7.2b	(pow.f64 (cbrt.f64 (fma.f64 x.re (.f64 -3 (.f64 x.im x.im)) (pow.f64 x.re 3))) 3)
	12.4b	(fma.f64 x.im (cbrt.f64 (pow.f64 (.f64 (.f64 x.im x.re) -3) 3)) (pow.f64 x.re 3))
	24.2b	(fma.f64 x.im (pow.f64 (sqrt.f64 (.f64 (.f64 x.im x.re) -3)) 2) (pow.f64 x.re 3))
▶	0.5b	(fma.f64 x.im (pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3) (pow.f64 x.re 3))

Compiler

Compiled 822 to 516 computations (37.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x.im (pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3) (pow.f64 x.re 3))
✓	0.2b	(.f64 (.f64 x.im x.re) -3)
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3)
✓	12.4b	(cbrt.f64 (.f64 (.f64 x.im x.re) -3))

series889.0ms (24.1%)

Counts

4 → 96

Calls

4 calls:

381.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3)
331.0ms	(cbrt.f64 (.f64 (.f64 x.im x.re) -3))
172.0ms	(fma.f64 x.im (pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3) (pow.f64 x.re 3))
5.0ms	(.f64 (.f64 x.im x.re) -3)

rewrite50.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

850×	`log1p-expm1-u_binary64`
850×	`expm1-log1p-u_binary64`
188×	`prod-diff_binary64`
99×	`egg-rr`
97×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	225	37
2	2415	37

Stop Event

1×	node limit

Counts

4 → 99

Calls

4 calls:

48.0ms	(fma.f64 x.im (pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3) (pow.f64 x.re 3))
48.0ms	(.f64 (.f64 x.im x.re) -3)
48.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3)
48.0ms	(cbrt.f64 (.f64 (.f64 x.im x.re) -3))

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

284×	`*-commutative_binary64`
269×	`unsub-neg_binary64`
264×	`unswap-sqr_binary64`
242×	`fma-def_binary64`
202×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	70	1956
1	188	1950
2	573	1821
3	1614	918
4	3466	910

Stop Event

1×	node limit

Counts

195 → 113

prune107.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	112	8	120

Error

0.0b

Counts

120 → 8

Alt Table

Status	Error	Program
✓	6.6b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))
	6.7b	(-.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))
	0.5b	(fma.f64 x.im (.f64 (pow.f64 (cbrt.f64 x.im) 2) (.f64 (cbrt.f64 x.im) (*.f64 x.re -3))) (pow.f64 x.re 3))
✓	0.1b	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
▶	0.2b	(fma.f64 -3 (.f64 x.im (.f64 x.im x.re)) (pow.f64 x.re 3))
	7.2b	(pow.f64 (cbrt.f64 (fma.f64 x.re (.f64 -3 (.f64 x.im x.im)) (pow.f64 x.re 3))) 3)
	12.4b	(fma.f64 x.im (cbrt.f64 (pow.f64 (.f64 (.f64 x.im x.re) -3) 3)) (pow.f64 x.re 3))
	24.2b	(fma.f64 x.im (pow.f64 (sqrt.f64 (.f64 (.f64 x.im x.re) -3)) 2) (pow.f64 x.re 3))

Compiler

Compiled 2113 to 1458 computations (31% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series21.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 -3 (.f64 x.im (.f64 x.im x.re)) (pow.f64 x.re 3))
9.0ms	(.f64 x.im (.f64 x.im x.re))

rewrite37.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

748×	`log1p-expm1-u_binary64`
748×	`expm1-log1p-u_binary64`
140×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	185	21
2	2089	21

Stop Event

1×	node limit

Counts

2 → 38

Calls

2 calls:

36.0ms	(fma.f64 -3 (.f64 x.im (.f64 x.im x.re)) (pow.f64 x.re 3))
36.0ms	(.f64 x.im (.f64 x.im x.re))

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
593×	`unswap-sqr_binary64`
340×	`fma-neg_binary64`
336×	`cancel-sign-sub-inv_binary64`
254×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	498
1	35	498
2	88	462
3	246	462
4	710	462
5	1445	462
6	2166	462
7	3399	462

Stop Event

1×	node limit

Counts

86 → 45

prune45.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	45	8	53

Error

0.0b

Counts

53 → 8

Alt Table

Status	Error	Program
✓	6.6b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))
	6.7b	(-.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))
	7.2b	(pow.f64 (cbrt.f64 (fma.f64 x.re (.f64 -3 (.f64 x.im x.im)) (pow.f64 x.re 3))) 3)
	6.6b	(fma.f64 -3 (*.f64 x.re (pow.f64 x.im 2)) (pow.f64 x.re 3))
	0.5b	(fma.f64 x.im (.f64 (pow.f64 (cbrt.f64 x.im) 2) (.f64 (cbrt.f64 x.im) (*.f64 x.re -3))) (pow.f64 x.re 3))
✓	0.1b	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
✓	0.2b	(fma.f64 -3 (.f64 x.im (.f64 x.im x.re)) (pow.f64 x.re 3))
	12.4b	(fma.f64 x.im (cbrt.f64 (pow.f64 (.f64 (.f64 x.im x.re) -3) 3)) (pow.f64 x.re 3))

Compiler

Compiled 751 to 422 computations (43.8% saved)

regimes155.0ms (4.2%)

Accuracy

Total 0.2b remaining (88.6%)

Threshold costs 0.2b (88.6%)

Counts

55 → 1

Compiler

Compiled 2319 to 1617 computations (30.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	11	14

Stop Event

1×

saturated

end110.0ms (3%)

Compiler: Compiled 141 to 94 computations (33.3% saved)

Details

analyze176.0ms (4.8%)

sample1.7s (44.9%)

simplify22.0ms (0.6%)

prune5.0ms (0.1%)

localize6.0ms (0.2%)

series14.0ms (0.4%)

rewrite43.0ms (1.2%)

simplify40.0ms (1.1%)

prune44.0ms (1.2%)

localize10.0ms (0.3%)

series15.0ms (0.4%)

rewrite41.0ms (1.1%)

simplify43.0ms (1.2%)

prune45.0ms (1.2%)

localize11.0ms (0.3%)

series889.0ms (24.1%)

rewrite50.0ms (1.3%)

simplify55.0ms (1.5%)

prune107.0ms (2.9%)

localize6.0ms (0.2%)

series21.0ms (0.6%)

rewrite37.0ms (1%)

simplify41.0ms (1.1%)

prune45.0ms (1.2%)

regimes155.0ms (4.2%)

simplify2.0ms (0%)

end110.0ms (3%)

Profiling