Details

analyze252.0ms (13.1%)

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
37.5%	50%	12.6%	6
43.7%	40.6%	15.7%	7
56.2%	23.4%	20.4%	8
57.8%	21.1%	21.2%	9
64%	12.5%	23.5%	10
64.8%	10.7%	24.5%	11
67.9%	6.4%	25.7%	12
68.3%	5.4%	26.3%	13
69.9%	3.3%	26.9%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample838.0ms (43.6%)

Results

748.0ms	8256×	body	128	valid
23.0ms	166×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify28.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

388×	`fma-def_binary64`
286×	`fma-neg_binary64`
71×	`distribute-rgt-in_binary64`
70×	`associate-l_binary64`
69×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	18	10
2	40	10
3	88	10
4	154	10
5	217	10
6	386	10
7	511	10
8	657	10
9	727	10
10	777	10
11	724	10

prune6.0ms (0.3%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (.f64 x (-.f64 x y)))
▶	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 58 to 37 computations (36.2% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
✓	0.0b	(-.f64 (.f64 x x) (.f64 x y))

series13.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

8.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
5.0ms	(-.f64 (.f64 x x) (.f64 x y))

rewrite58.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

885×	`log1p-expm1-u_binary64`
885×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
85×	`add-log-exp_binary64`
84×	`add-cube-cbrt_binary64`

Counts

2 → 74

Calls

2 calls:

57.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
57.0ms	(-.f64 (.f64 x x) (.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	179	17
2	2233	17
3	5327	17
0	0	0
1	0	0

simplify139.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

952×	`fma-neg_binary64`
477×	`distribute-rgt-neg-in_binary64`
415×	`neg-mul-1_binary64`
398×	`associate-l_binary64`
323×	`distribute-lft-neg-in_binary64`

Counts

122 → 85

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	486
1	41	378
2	85	378
3	193	378
4	463	378
5	1330	378
6	2262	378
7	3720	378
8	4561	378
9	4926	378
10	4995	378
11	4875	378

prune50.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	84	3	87

Error

Counts

87 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 x (.f64 2 (-.f64 x y)))
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
	0.3b	(.f64 2 (fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (.f64 x y))))

Compiler

Compiled 1284 to 536 computations (58.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(*.f64 x (*.f64 2 (-.f64 x y)))

rewrite47.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

767×	`log1p-expm1-u_binary64`
767×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
78×	`add-sqr-sqrt_binary64`
73×	`add-log-exp_binary64`

Counts

1 → 19

Calls

1 calls:

46.0ms

(*.f64 x (*.f64 2 (-.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	153	10
2	1930	10
3	5356	10
0	0	0
1	0	0

simplify98.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-neg_binary64`
534×	`fma-def_binary64`
453×	`distribute-rgt-neg-in_binary64`
382×	`neg-mul-1_binary64`
377×	`neg-sub0_binary64`

Counts

43 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	276
1	31	222
2	72	222
3	165	222
4	415	222
5	1182	222
6	2315	222
7	3491	222
8	4278	222
9	4933	222
10	4866	222

prune13.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	24	3	27

Error

Counts

27 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
▶	0.3b	(.f64 2 (fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (.f64 x y))))

Compiler

Compiled 299 to 181 computations (39.5% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (.f64 x y))))
✓	0.0b	(fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (*.f64 x y)))
✓	52.0b	(fma.f64 (neg.f64 y) x (*.f64 x y))

series26.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

10.0ms	(.f64 2 (fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (.f64 x y))))
9.0ms	(fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (*.f64 x y)))
7.0ms	(fma.f64 (neg.f64 y) x (*.f64 x y))

rewrite64.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

946×	`prod-diff_binary64`
900×	`expm1-log1p-u_binary64`
109×	`add-sqr-sqrt_binary64`
103×	`log1p-expm1-u_binary64`
100×	`add-cbrt-cube_binary64`

Counts

3 → 61

Calls

3 calls:

63.0ms	(.f64 2 (fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (.f64 x y))))
63.0ms	(fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (*.f64 x y)))
63.0ms	(fma.f64 (neg.f64 y) x (*.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	47
1	214	38
2	2326	38
3	5602	38
0	0	0
1	0	0

simplify128.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

952×	`fma-neg_binary64`
477×	`distribute-rgt-neg-in_binary64`
415×	`neg-mul-1_binary64`
398×	`associate-l_binary64`
323×	`distribute-lft-neg-in_binary64`

Counts

133 → 74

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	510
1	42	402
2	85	402
3	193	402
4	463	402
5	1330	402
6	2262	402
7	3720	402
8	4561	402
9	4926	402
10	4995	402
11	4875	402

prune31.0ms (1.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	74	3	77

Error

Counts

77 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
✓	0.3b	(.f64 2 (fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (.f64 x y))))

Compiler

Compiled 1160 to 402 computations (65.3% saved)

regimes56.0ms (2.9%)

Accuracy

Total 0.0b remaining (90.7%)

Threshold costs 0.0b (90.7%)

Counts

13 → 1

Compiler

Compiled 632 to 404 computations (36.1% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	25	13
3	31	13
4	35	13
5	36	13
6	36	13

end47.0ms (2.4%)

Compiler: Compiled 58 to 36 computations (37.9% saved)

Iter	Nodes	Cost
0	8	10
1	18	10
2	40	10
3	88	10
4	154	10
5	217	10
6	386	10
7	511	10
8	657	10
9	727	10
10	777	10
11	724	10

Iter	Nodes	Cost
0	8	10
1	18	10
2	40	10
3	88	10
4	154	10
5	217	10
6	386	10
7	511	10
8	657	10
9	727	10
10	777	10
11	724	10

Details

analyze252.0ms (13.1%)

sample838.0ms (43.6%)

simplify28.0ms (1.5%)

prune6.0ms (0.3%)

localize5.0ms (0.3%)

series13.0ms (0.7%)

rewrite58.0ms (3%)

simplify139.0ms (7.2%)

prune50.0ms (2.6%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite47.0ms (2.4%)

simplify98.0ms (5.1%)

prune13.0ms (0.7%)

localize8.0ms (0.4%)

series26.0ms (1.4%)

rewrite64.0ms (3.3%)

simplify128.0ms (6.7%)

prune31.0ms (1.6%)

regimes56.0ms (2.9%)

simplify3.0ms (0.2%)

end47.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	8	10
1	18	10
2	40	10
3	88	10
4	154	10
5	217	10
6	386	10
7	511	10
8	657	10
9	727	10
10	777	10
11	724	10