Details

analyze4.0ms (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)

sample823.0ms (62.8%)

Results

776.0ms	8256×	body	128	valid
0.0ms	4×	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))

series8.0ms (0.6%)

Counts

1 → 4

Calls

1 calls:

8.0ms

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

rewrite135.0ms (10.3%)

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:

134.0ms

(*.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

simplify64.0ms (4.9%)

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

prune13.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	3	26

Error

Counts

26 → 3

Alt Table

Status	Error	Program
	38.8b	(sqrt.f64 (*.f64 x (-.f64 x 1)))
▶	0.3b	(-.f64 x 1/2)
✓	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 276 to 211 computations (23.6% saved)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
▶	38.8b	(sqrt.f64 (*.f64 x (-.f64 x 1)))
✓	0.3b	(-.f64 x 1/2)
✓	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 26 to 19 computations (26.9% saved)

localize20.0ms (1.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	36.0b	(sqrt.f64 (*.f64 x (-.f64 x 1)))

series4.0ms (0.3%)

Counts

1 → 8

Calls

1 calls:

4.0ms

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

rewrite55.0ms (4.2%)

Algorithm

2×	batch-egg-rewrite

Rules

545×	`log1p-expm1-u_binary64`
545×	`expm1-log1p-u_binary64`
484×	`unpow-prod-down_binary64`
267×	`log-prod_binary64`
143×	`pow2_binary64`

Counts

1 → 52

Calls

1 calls:

54.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	125	9
2	1402	9
3	5484	9
0	0	0
1	0	0

simplify56.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

676×	`times-frac_binary64`
590×	`fma-neg_binary64`
572×	`div-sub_binary64`
545×	`associate-/r*_binary64`
427×	`cancel-sign-sub-inv_binary64`

Counts

60 → 65

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	70
1	58	70
2	130	70
3	327	70
4	711	70
5	1486	70
6	4461	70
7	5094	70

prune29.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	65	3	68

Error

Counts

68 → 3

Alt Table

Status	Error	Program
✓	38.8b	(sqrt.f64 (*.f64 x (-.f64 x 1)))
✓	0.3b	(-.f64 x 1/2)
✓	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 834 to 620 computations (25.7% saved)

regimes14.0ms (1.1%)

Accuracy

Total 0.5b remaining (99.8%)

Threshold costs 0.5b (99.8%)

Counts

4 → 1

Compiler

Compiled 62 to 44 computations (29% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	7	4
2	8	4
3	7	4

end70.0ms (5.4%)

Compiler: Compiled 27 to 20 computations (25.9% saved)

Details

analyze4.0ms (0.3%)

sample823.0ms (62.8%)

simplify6.0ms (0.4%)

prune1.0ms (0.1%)

localize4.0ms (0.3%)

series8.0ms (0.6%)

rewrite135.0ms (10.3%)

simplify64.0ms (4.9%)

prune13.0ms (1%)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

localize20.0ms (1.5%)

series4.0ms (0.3%)

rewrite55.0ms (4.2%)

simplify56.0ms (4.2%)

prune29.0ms (2.2%)

regimes14.0ms (1.1%)

simplify2.0ms (0.1%)

end70.0ms (5.4%)

Profiling