Details

sample66.0ms

Algorithm

intervals

Results

24.0ms	195×	body	80	valid
11.0ms	23×	body	2560	valid
5.0ms	9×	body	5120	valid
4.0ms	8×	body	1280	valid
3.0ms	10×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	1×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.2b	(+ (hypot re im) re)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

0.0ms	(hypot re im)
7.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms	(+ (hypot re im) re)

series416.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(hypot re im)
278.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
77.0ms	(+ (hypot re im) re)

simplify1.8s

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
3	1417
2	484
1	187
0	86

prune365.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
9.4b	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`pow1/3`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
2.0ms	(cbrt (hypot re im))
38.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series660.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (hypot re im))
206.0ms	(cbrt (hypot re im))
205.0ms	(cbrt (hypot re im))
87.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify3.6s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
4	4643
3	1326
2	430
1	151
0	63

prune430.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
14.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

4 → 43

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
6.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series597.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(hypot re im)
62.0ms	(hypot re im)
305.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
174.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify3.0s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
4	3497
3	1098
2	369
1	149
0	74

prune475.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
14.9b	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)

series747.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (hypot re im))
178.0ms	(cbrt (hypot re im))
186.0ms	(cbrt (hypot re im))
214.0ms	(fma (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) re)

simplify2.1s

Counts

61 → 61

Iterations

Iter	Nodes
done	5002
4	2318
3	735
2	239
1	103
0	56

prune440.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 13.0b

regimes213.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample1.9s

Algorithm

intervals

Results

587.0ms	488×	body	1280	valid
558.0ms	6019×	body	80	valid
336.0ms	682×	body	2560	valid
116.0ms	290×	body	5120	valid
71.0ms	297×	body	640	valid
26.0ms	143×	body	320	valid
9.0ms	81×	body	160	valid