Details

sample29.0ms

Algorithm

intervals

Results

7.0ms	187×	body	80	valid
5.0ms	24×	body	2560	valid
4.0ms	21×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	10×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	30	10
3	32	10
done	32	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
0.7b	(+ re (hypot re im))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

8.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
6.0ms	(+ re (hypot re im))

series244.0ms

Counts

2 → 6

Calls

2 calls:

186.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
59.0ms	(+ re (hypot re im))

simplify2.9s

Counts

38 → 38

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	75	354
1	173	325
2	444	302
3	1193	293
4	3103	292
done	5000	292

prune96.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
16.5b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

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

series714.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt re)
175.0ms	(cbrt re)
174.0ms	(cbrt re)
184.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify796.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	42	372
1	62	360
2	121	286
3	329	244
4	1216	244
done	5000	244

prune177.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 14.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
16.4b	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (hypot re im))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

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

series714.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt re)
176.0ms	(cbrt re)
177.0ms	(cbrt re)
185.0ms	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (hypot re im))

simplify1.1s

Counts

61 → 61

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	44	489
1	70	477
2	152	331
3	419	244
4	1869	244
done	5001	244

prune211.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 14.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
16.4b	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))))) (hypot re im))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

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

series904.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt re)
374.0ms	(cbrt re)
176.0ms	(cbrt re)
184.0ms	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))))) (hypot re im))

simplify1.1s

Counts

61 → 61

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	46	606
1	75	594
2	165	430
3	478	244
4	1895	244
done	5002	244

prune224.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 14.6b

regimes56.0ms

Accuracy

0% (0.2b remaining)

Error of 13.5b against oracle of 13.3b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	12	10
done	12	10

end0.0ms

sample778.0ms

Algorithm

intervals

Results

213.0ms	5985×	body	80	valid
158.0ms	722×	body	2560	valid
83.0ms	478×	body	1280	valid
74.0ms	290×	body	5120	valid
38.0ms	284×	body	640	valid
17.0ms	142×	body	320	valid
7.0ms	99×	body	160	valid