Details

analyze5.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	50%	50%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample929.0ms (58%)

Results

818.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	14	11
3	12	11

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

series55.0ms (3.4%)

Counts

1 → 4

Calls

1 calls:

55.0ms

(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

rewrite73.0ms (4.5%)

Algorithm

2×	batch-egg-rewrite

Rules

602×	`log1p-expm1-u_binary64`
602×	`expm1-log1p-u_binary64`
297×	`log-prod_binary64`
128×	`fma-def_binary64`
111×	`expm1-udef_binary64`

Counts

1 → 19

Calls

1 calls:

72.0ms

(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	144	9
2	1557	9
3	4977	9
4	4958	9
0	0	0
1	0	0

simplify65.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

676×	`times-frac_binary64`
647×	`sub-neg_binary64`
551×	`fma-neg_binary64`
545×	`associate-/r*_binary64`
457×	`fma-def_binary64`

Counts

23 → 25

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	34
1	44	34
2	99	34
3	237	34
4	555	34
5	1313	34
6	4205	34
7	4870	34
8	5476	34

prune17.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	2	26

Error

Counts

26 → 2

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
✓	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 282 to 215 computations (23.8% saved)

localize8.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
✓	0.5b	(/.f64 1/16 (*.f64 x x))

series5.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
2.0ms	(/.f64 1/16 (*.f64 x x))

rewrite65.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

926×	`prod-diff_binary64`
166×	`expm1-udef_binary64`
166×	`log1p-udef_binary64`
95×	`log1p-expm1-u_binary64`
95×	`expm1-log1p-u_binary64`

Counts

2 → 88

Calls

2 calls:

63.0ms	(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
63.0ms	(/.f64 1/16 (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	194	18
2	2624	18
3	4822	18
0	0	0
1	0	0

simplify127.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

1160×	`associate-/r/_binary64`
712×	`*-commutative_binary64`
697×	`fma-def_binary64`
593×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`

Counts

112 → 92

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	216
1	26	216
2	38	216
3	63	216
4	129	216
5	354	216
6	1391	216
7	2333	216
8	2553	216
9	2835	216
10	3168	216
11	3429	216
12	3703	216
13	3931	216
14	4877	216
15	4754	216

prune144.0ms (9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	92	2	94

Error

Counts

94 → 2

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
✓	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 1758 to 1188 computations (32.4% saved)

regimes37.0ms (2.3%)

Accuracy

Total 0.3b remaining (98.3%)

Threshold costs 0.3b (98.3%)

Counts

17 → 1

Compiler

Compiled 342 to 264 computations (22.8% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`distribute-neg-in_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	14	17
2	24	17
3	29	17
4	32	17
5	33	17
6	32	17

end59.0ms (3.7%)

Compiler: Compiled 48 to 36 computations (25% saved)

Details

analyze5.0ms (0.3%)

sample929.0ms (58%)

simplify6.0ms (0.4%)

prune1.0ms (0.1%)

localize4.0ms (0.3%)

series55.0ms (3.4%)

rewrite73.0ms (4.5%)

simplify65.0ms (4.1%)

prune17.0ms (1.1%)

localize8.0ms (0.5%)

series5.0ms (0.3%)

rewrite65.0ms (4%)

simplify127.0ms (7.9%)

prune144.0ms (9%)

regimes37.0ms (2.3%)

simplify2.0ms (0.2%)

end59.0ms (3.7%)

Profiling