Details

analyze90.0ms (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
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)

sample794.0ms (42.1%)

Results

719.0ms	8256×	body	128	valid
13.0ms	169×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify26.0ms (1.4%)

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

prune5.0ms (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 (.f64 x x) (*.f64 x y)))
▶	0.0b	(.f64 2 (.f64 x (-.f64 x y)))

Compiler

Compiled 58 to 37 computations (36.2% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(.f64 2 (.f64 x (-.f64 x y)))
5.0ms	(*.f64 x (-.f64 x y))

rewrite29.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`

Counts

2 → 124

Calls

2 calls:

11.0ms	(.f64 2 (.f64 x (-.f64 x y)))
6.0ms	(*.f64 x (-.f64 x y))

simplify117.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

420×	`*-commutative_binary64`
359×	`fma-neg_binary64`
354×	`exp-prod_binary64`
320×	`distribute-lft-neg-out_binary64`
318×	`distribute-rgt-neg-out_binary64`

Counts

172 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	209	2517
1	289	2040
2	976	1878
3	2563	1715
4	4557	1715
5	4998	1715
6	4713	1715

prune91.0ms (4.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	154	3	157

Error

Counts

157 → 3

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
	17.4b	(.f64 2 (.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y)))))
▶	0.0b	(.f64 x (.f64 2 (-.f64 x y)))

Compiler

Compiled 3068 to 1068 computations (65.2% 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)))

series8.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite16.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`distribute-lft-in_binary64`
52×	`distribute-rgt-in_binary64`
36×	`prod-diff_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`

Counts

1 → 74

Calls

1 calls:

8.0ms

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

simplify87.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

510×	`fma-neg_binary64`
381×	`*-commutative_binary64`
334×	`exp-prod_binary64`
295×	`distribute-lft-neg-out_binary64`
290×	`distribute-rgt-neg-out_binary64`

Counts

98 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	1726
1	260	1429
2	790	1213
3	2192	1105
4	4566	1105
5	4891	1105

prune44.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

Counts

87 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
	17.4b	(.f64 2 (.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y)))))
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))

Compiler

Compiled 1861 to 742 computations (60.1% 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))

series15.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
6.0ms	(-.f64 (.f64 x x) (.f64 x y))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 46

Calls

2 calls:

5.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
3.0ms	(-.f64 (.f64 x x) (.f64 x y))

simplify71.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-neg_binary64`
500×	`associate-l_binary64`
430×	`associate-r_binary64`
208×	`fma-def_binary64`
177×	`distribute-rgt-neg-out_binary64`

Counts

94 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	1026
1	193	954
2	582	936
3	2421	936
4	4654	936
5	4890	936

prune43.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	87	3	90

Error

Counts

90 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
▶	17.4b	(.f64 2 (.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y)))))
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))

Compiler

Compiled 1295 to 475 computations (63.3% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 x (-.f64 x y))
✓	0.1b	(.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))))
✓	8.6b	(sqrt.f64 (*.f64 x (-.f64 x y)))

series33.0ms (1.8%)

Counts

2 → 36

Calls

2 calls:

28.0ms	(sqrt.f64 (*.f64 x (-.f64 x y)))
5.0ms	(.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))))

rewrite25.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`pow1_binary64`
30×	`sqrt-pow1_binary64`
21×	`pow-prod-down_binary64`
16×	`associate-*r/_binary64`
14×	`sqrt-div_binary64`

Counts

2 → 74

Calls

2 calls:

10.0ms	(.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))))
7.0ms	(sqrt.f64 (*.f64 x (-.f64 x y)))

simplify98.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

613×	`unswap-sqr_binary64`
601×	`times-frac_binary64`
563×	`associate-l_binary64`
454×	`fma-neg_binary64`
407×	`associate-r_binary64`

Counts

110 → 101

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	101	1377
1	207	1206
2	647	1154
3	2696	1128
4	4307	1108
5	4936	1108
6	4976	1108

prune142.0ms (7.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	258	0	258
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	258	3	261

Error

Counts

261 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
✓	17.4b	(.f64 2 (.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y)))))
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))

Compiler

Compiled 5918 to 1696 computations (71.3% saved)

regimes64.0ms (3.4%)

Accuracy

Total 0.0b remaining (80.7%)

Threshold costs 0.0b (80.7%)

Counts

17 → 1

Compiler

Compiled 780 to 524 computations (32.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	16	10
3	18	10
4	19	10
5	19	10

end43.0ms (2.3%)

Compiler: Compiled 55 to 33 computations (40% 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

analyze90.0ms (4.8%)

sample794.0ms (42.1%)

simplify26.0ms (1.4%)

prune5.0ms (0.3%)

localize4.0ms (0.2%)

series15.0ms (0.8%)

rewrite29.0ms (1.5%)

simplify117.0ms (6.2%)

prune91.0ms (4.8%)

localize4.0ms (0.2%)

series8.0ms (0.4%)

rewrite16.0ms (0.8%)

simplify87.0ms (4.6%)

prune44.0ms (2.3%)

localize5.0ms (0.3%)

series15.0ms (0.8%)

rewrite10.0ms (0.5%)

simplify71.0ms (3.7%)

prune43.0ms (2.3%)

localize6.0ms (0.3%)

series33.0ms (1.8%)

rewrite25.0ms (1.3%)

simplify98.0ms (5.2%)

prune142.0ms (7.5%)

regimes64.0ms (3.4%)

simplify2.0ms (0.1%)

end43.0ms (2.3%)

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