Details

analyze241.0ms (14.1%)

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%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample873.0ms (51.2%)

Symmetry

(sort x y)

Results

835.0ms	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	9	8
3	9	8

prune6.0ms (0.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x x (*.f64 y y))

Compiler

Compiled 31 to 14 computations (54.8% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(fma.f64 x x (*.f64 y y))

rewrite75.0ms (4.4%)

Algorithm

2×	batch-egg-rewrite

Rules

726×	`log1p-udef_binary64`
401×	`log1p-expm1-u_binary64`
401×	`expm1-log1p-u_binary64`
345×	`pow1_binary64`
254×	`unpow-prod-down_binary64`

Counts

1 → 36

Calls

1 calls:

74.0ms

(fma.f64 x x (*.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	98	7
2	1061	7
3	4611	7
4	5882	7
0	0	0
1	0	0

simplify124.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

1238×	`sqr-pow_binary64`
688×	`fabs-mul_binary64`
666×	`cube-prod_binary64`
532×	`pow-sqr_binary64`
344×	`unpow3_binary64`

Counts

60 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	204
1	16	168
2	25	168
3	43	168
4	91	168
5	211	168
6	629	168
7	736	168
8	898	168
9	1111	168
10	1382	168
11	1719	168
12	2150	168
13	2616	168
14	3366	168
15	3655	168
16	3998	168
17	4131	168
18	4182	168
19	4210	168
20	5084	168

prune22.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	2	43

Error

Counts

43 → 2

Alt Table

Status	Error	Program
▶	0.0b	(pow.f64 (hypot.f64 x y) 2)
✓	0.0b	(fma.f64 x x (*.f64 y y))

Compiler

Compiled 427 to 239 computations (44% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 x y) 2)

series36.0ms (2.1%)

Counts

1 → 24

Calls

1 calls:

36.0ms

(pow.f64 (hypot.f64 x y) 2)

rewrite72.0ms (4.2%)

Algorithm

2×	batch-egg-rewrite

Rules

833×	`log1p-udef_binary64`
454×	`log1p-expm1-u_binary64`
454×	`expm1-log1p-u_binary64`
275×	`unpow-prod-down_binary64`
232×	`log-prod_binary64`

Counts

1 → 47

Calls

1 calls:

71.0ms

(pow.f64 (hypot.f64 x y) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	122	7
2	1201	7
3	4708	7
4	6053	7
0	0	0
1	0	0

simplify124.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

1238×	`sqr-pow_binary64`
688×	`fabs-mul_binary64`
666×	`cube-prod_binary64`
532×	`pow-sqr_binary64`
344×	`unpow3_binary64`

Counts

71 → 52

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	204
1	16	168
2	25	168
3	43	168
4	91	168
5	211	168
6	629	168
7	736	168
8	898	168
9	1111	168
10	1382	168
11	1719	168
12	2150	168
13	2616	168
14	3366	168
15	3655	168
16	3998	168
17	4131	168
18	4182	168
19	4210	168
20	5084	168

prune19.0ms (1.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	52	2	54

Error

Counts

54 → 2

Alt Table

Status	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 x y) 2)
✓	0.0b	(fma.f64 x x (*.f64 y y))

Compiler

Compiled 526 to 249 computations (52.7% saved)

regimes52.0ms (3%)

Accuracy

Total 0.0b remaining (88.3%)

Threshold costs 0.0b (88.3%)

Counts

8 → 1

Compiler

Compiled 394 to 240 computations (39.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	6	7

end41.0ms (2.4%)

Remove: (sort x y)
Compiler: Compiled 43 to 29 computations (32.6% saved)

Details

analyze241.0ms (14.1%)

sample873.0ms (51.2%)

simplify6.0ms (0.4%)

prune6.0ms (0.4%)

localize3.0ms (0.2%)

series6.0ms (0.3%)

rewrite75.0ms (4.4%)

simplify124.0ms (7.3%)

prune22.0ms (1.3%)

localize3.0ms (0.2%)

series36.0ms (2.1%)

rewrite72.0ms (4.2%)

simplify124.0ms (7.3%)

prune19.0ms (1.1%)

regimes52.0ms (3%)

simplify2.0ms (0.1%)

end41.0ms (2.4%)

Profiling