Details

analyze177.0ms (7.5%)

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)

sample1.0s (44.3%)

Results

951.0ms	8256×	body	128	valid
47.0ms	411×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify20.0ms (0.9%)

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

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

6.6b

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 (0.3%)

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))

series13.0ms (0.6%)

Counts

2 → 36

Calls

2 calls:

11.0ms	(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))

rewrite40.0ms (1.7%)

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:

39.0ms	(.f64 x.im (.f64 x.im -3))
39.0ms	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))

simplify38.0ms (1.6%)

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 (1.9%)

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
	6.7b	(-.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)
▶	0.1b	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
✓	6.6b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))
	30.3b	(.f64 (.f64 x.im x.im) (*.f64 -3 x.re))

Compiler

Compiled 771 to 475 computations (38.4% saved)

localize6.0ms (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))

series17.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
4.0ms	(.f64 x.im (.f64 -3 x.re))

rewrite37.0ms (1.6%)

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:

37.0ms	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
36.0ms	(.f64 x.im (.f64 -3 x.re))

simplify40.0ms (1.7%)

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

prune49.0ms (2.1%)

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
	6.7b	(-.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)
✓	0.1b	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
✓	6.6b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (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))
	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)

localize9.0ms (0.4%)

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))

series189.0ms (8%)

Counts

4 → 31

Calls

4 calls:

90.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3)
57.0ms	(fma.f64 x.im (pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3) (pow.f64 x.re 3))
37.0ms	(cbrt.f64 (.f64 (.f64 x.im x.re) -3))
4.0ms	(.f64 (.f64 x.im x.re) -3)

rewrite48.0ms (2%)

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:

46.0ms	(fma.f64 x.im (pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3) (pow.f64 x.re 3))
46.0ms	(.f64 (.f64 x.im x.re) -3)
46.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x.im x.re) -3)) 3)
46.0ms	(cbrt.f64 (.f64 (.f64 x.im x.re) -3))

simplify78.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

729×	`sqr-pow_binary64`
410×	`cube-prod_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
283×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	196
1	20	196
2	32	196
3	43	196
4	64	196
5	154	196
6	503	196
7	1168	196
8	1255	196
9	1388	196
10	1546	196
11	1774	196
12	2096	196
13	2517	196
14	3017	196
15	3612	196
16	4336	196
17	4661	196
18	4945	196

Stop Event

1×	node limit

Counts

130 → 93

prune94.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	2	2	4
Picked	1	0	1
Done	1	1	2
Total	94	6	100

Error

0.0b

Counts

100 → 6

Alt Table

Status	Error	Program
	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 (.f64 -3 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)
✓	0.1b	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (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))
	0.3b	(fma.f64 x.im (.f64 (.f64 x.im x.re) (pow.f64 (cbrt.f64 -3) 3)) (pow.f64 x.re 3))

Compiler

Compiled 1717 to 1175 computations (31.6% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(fma.f64 x.im (.f64 (.f64 -3 x.im) x.re) (pow.f64 x.re 3))
4.0ms	(.f64 (.f64 -3 x.im) x.re)

rewrite36.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

764×	`log1p-expm1-u_binary64`
764×	`expm1-log1p-u_binary64`
176×	`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	2123	21

Stop Event

1×	node limit

Counts

2 → 38

Calls

2 calls:

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

simplify51.0ms (2.1%)

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

prune36.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	45	6	51

Error

0.0b

Counts

51 → 6

Alt Table

Status	Error	Program
	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 (.f64 -3 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)
✓	0.1b	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (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))
	0.3b	(fma.f64 x.im (.f64 (.f64 x.im x.re) (pow.f64 (cbrt.f64 -3) 3)) (pow.f64 x.re 3))

Compiler

Compiled 729 to 493 computations (32.4% saved)

regimes167.0ms (7.1%)

Accuracy

Total 0.1b remaining (78.4%)

Threshold costs 0.1b (78.4%)

Counts

56 → 1

Compiler

Compiled 2436 to 1695 computations (30.4% saved)

simplify2.0ms (0.1%)

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

end93.0ms (3.9%)

Compiler: Compiled 117 to 77 computations (34.2% saved)

Details

analyze177.0ms (7.5%)

sample1.0s (44.3%)

simplify20.0ms (0.9%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

series13.0ms (0.6%)

rewrite40.0ms (1.7%)

simplify38.0ms (1.6%)

prune44.0ms (1.9%)

localize6.0ms (0.3%)

series17.0ms (0.7%)

rewrite37.0ms (1.6%)

simplify40.0ms (1.7%)

prune49.0ms (2.1%)

localize9.0ms (0.4%)

series189.0ms (8%)

rewrite48.0ms (2%)

simplify78.0ms (3.3%)

prune94.0ms (4%)

localize6.0ms (0.3%)

series15.0ms (0.6%)

rewrite36.0ms (1.5%)

simplify51.0ms (2.1%)

prune36.0ms (1.5%)

regimes167.0ms (7.1%)

simplify2.0ms (0.1%)

end93.0ms (3.9%)

Profiling