Details

sample185.0ms

Algorithm

intervals

Results

31.0ms	198×	body	80	valid
18.0ms	24×	body	2560	valid
11.0ms	11×	body	5120	valid
6.0ms	11×	body	1280	valid
3.0ms	5×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify105.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	45
5	45
4	43
3	36
2	28
1	19
0	12

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (- (hypot re im) re) 2.0))
0.7b	(- (hypot re im) re)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`hypot-udef` `sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

0.0ms	(hypot re im)
19.0ms	(sqrt (* (- (hypot re im) re) 2.0))
11.0ms	(- (hypot re im) re)

series381.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(hypot re im)
230.0ms	(sqrt (* (- (hypot re im) re) 2.0))
95.0ms	(- (hypot re im) re)

simplify2.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	3929
2	771
1	248
0	118

prune355.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* (- (hypot re im) re) 2.0))
0.4b	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

76×	`sqrt-pow1`
64×	`pow1`
42×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`sqrt-prod`
26×	`sqrt-div` `add-cube-cbrt`
23×	`pow-prod-down`
19×	`pow1/2`
18×	`prod-diff`
16×	`associate-*l/`
14×	`pow-prod-up`
9×	`flip3--` `swap-sqr` `flip--`
8×	`pow-sqr` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`sub-neg` `diff-log` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

15.0ms	(sqrt (* (- (hypot re im) re) 2.0))
88.0ms	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
5.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)

series696.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(sqrt (* (- (hypot re im) re) 2.0))
265.0ms	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
72.0ms	(- (hypot re im) re)
96.0ms	(- (hypot re im) re)

simplify1.5s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	1513
1	398
0	184

prune684.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

10.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)

series359.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (hypot re im) re)
95.0ms	(- (hypot re im) re)
90.0ms	(- (hypot re im) re)
103.0ms	(- (hypot re im) re)

simplify1.4s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
3	1490
2	328
1	131
0	62

prune857.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.4b

localize108.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
13.8b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 98

Calls

4 calls:

9.0ms	(- (hypot re im) re)
9.0ms	(- (hypot re im) re)
10.0ms	(- (hypot re im) re)
1.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series511.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (hypot re im) re)
104.0ms	(- (hypot re im) re)
83.0ms	(- (hypot re im) re)
248.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify2.6s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
3	2388
2	406
1	155
0	77

prune818.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.4b

regimes147.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	6088×	body	80	valid
542.0ms	616×	body	2560	valid
326.0ms	510×	body	1280	valid
287.0ms	282×	body	5120	valid
124.0ms	274×	body	640	valid
57.0ms	155×	body	320	valid
17.0ms	75×	body	160	valid