Details

sample49.0ms

Algorithm

intervals

Results

13.0ms	193×	body	80	valid
12.0ms	29×	body	2560	valid
4.0ms	7×	body	5120	valid
4.0ms	10×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	31
3	31
2	29
1	24
0	12

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.0b

localize43.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
1.0b	(+ (hypot re im) re)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `sqrt-div` `associate-*l/` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

2 → 34

Calls

2 calls:

16.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
12.0ms	(+ (hypot re im) re)

series330.0ms

Counts

2 → 6

Calls

2 calls:

250.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
80.0ms	(+ (hypot re im) re)

simplify3.2s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
4	4643
3	1359
2	470
1	176
0	77

prune189.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (hypot re im) re))
1.0b	(+ (hypot re im) re)
1.0b	(+ (hypot re im) re)
1.0b	(+ (hypot re im) re)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`fma-def`
8×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`cbrt-prod` `expm1-log1p-u` `pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`+-commutative` `sum-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 71

Calls

4 calls:

6.0ms	(cbrt (+ (hypot re im) re))
9.0ms	(+ (hypot re im) re)
6.0ms	(+ (hypot re im) re)
6.0ms	(+ (hypot re im) re)

series484.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(cbrt (+ (hypot re im) re))
86.0ms	(+ (hypot re im) re)
81.0ms	(+ (hypot re im) re)
107.0ms	(+ (hypot re im) re)

simplify2.8s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
4	4287
3	1282
2	461
1	187
0	84

prune555.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
1.0b	(+ (hypot re im) re)
1.0b	(+ (hypot re im) re)
15.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`fma-def`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-prod`
2×	`+-commutative` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`
1×	`pow1/3` `fma-udef`

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
11.0ms	(+ (hypot re im) re)
12.0ms	(+ (hypot re im) re)
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series576.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
89.0ms	(+ (hypot re im) re)
69.0ms	(+ (hypot re im) re)
173.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.8s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1880
2	676
1	254
0	108

prune660.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.9b

localize110.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (hypot re im) re)
15.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
15.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
15.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `fma-udef`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

12.0ms	(+ (hypot re im) re)
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series761.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (hypot re im) re)
223.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
223.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
224.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify2.3s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
4	2471
3	823
2	327
1	123
0	53

prune605.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.9b

regimes135.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

786.0ms	712×	body	2560	valid
440.0ms	5971×	body	80	valid
245.0ms	492×	body	1280	valid
240.0ms	320×	body	5120	valid
105.0ms	155×	body	320	valid
67.0ms	257×	body	640	valid
12.0ms	93×	body	160	valid