Details

sample301.0ms

Algorithm

intervals

Results

155.0ms	192×	body	80	valid
43.0ms	13×	body	2560	valid
16.0ms	14×	body	5120	valid
15.0ms	19×	body	1280	valid
5.0ms	8×	body	640	valid
2.0ms	5×	body	320	valid
2.0ms	5×	body	160	valid

simplify148.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	42
3	35
2	27
1	19
0	12

prune56.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize651.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
1.3b	(- (hypot re im) re)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

17.0ms	(sqrt (* (- (hypot re im) re) 2.0))
14.0ms	(- (hypot re im) re)

series453.0ms

Counts

2 → 6

Calls

2 calls:

308.0ms	(sqrt (* (- (hypot re im) re) 2.0))
144.0ms	(- (hypot re im) re)

simplify1.3s

Counts

51 → 51

Iterations

Iter	Nodes
done	2006
4	2006
3	1768
2	551
1	237
0	109

prune540.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
9.6b	(- (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) re)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`cbrt-prod`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`prod-diff`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `fma-neg` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--`

Counts

4 → 90

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
16.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
53.0ms	(- (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) re)

series561.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt (hypot re im))
159.0ms	(cbrt (hypot re im))
157.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
85.0ms	(- (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) re)

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	2004
4	2004
3	1772
2	667
1	286
0	128

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im))))
0.5b	(* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im))))
0.5b	(* (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
12.5b	(- (* (cbrt (hypot re im)) (* (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) re)

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
47×	`pow1`
38×	`cbrt-prod` `sqrt-prod`
20×	`add-exp-log`
19×	`associate-r` `associate-l` `pow-prod-down`
18×	`unswap-sqr`
17×	`*-un-lft-identity` `add-cube-cbrt`
14×	`add-cbrt-cube`
10×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u`
3×	`swap-sqr` `prod-diff` `*-commutative`
2×	`pow-plus`
1×	`pow2` `sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 140

Calls

4 calls:

23.0ms	(* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im))))
22.0ms	(* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im))))
66.0ms	(* (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
156.0ms	(- (* (cbrt (hypot re im)) (* (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) re)

series627.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im))))
160.0ms	(* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im))))
213.0ms	(* (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
110.0ms	(- (* (cbrt (hypot re im)) (* (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) re)

simplify1.2s

Counts

152 → 152

Iterations

Iter	Nodes
done	2005
3	2005
2	992
1	357
0	158

prune2.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.6b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
0.5b	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
0.5b	(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
12.5b	(- (* (cbrt (hypot re im)) (* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) re)

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

129×	`pow1`
80×	`cbrt-prod`
73×	`add-sqr-sqrt`
56×	`pow1/3`
53×	`pow-prod-up`
40×	`sqrt-prod`
37×	`pow-sqr`
36×	`pow-prod-down`
29×	`*-un-lft-identity` `add-cube-cbrt`
23×	`swap-sqr`
20×	`pow-plus` `add-exp-log`
19×	`associate-r` `associate-l` `unswap-sqr`
15×	`pow2`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`prod-diff` `*-commutative`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 214

Calls

4 calls:

20.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
22.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
63.0ms	(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
128.0ms	(- (* (cbrt (hypot re im)) (* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) re)

series541.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
144.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
172.0ms	(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
83.0ms	(- (* (cbrt (hypot re im)) (* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) re)

simplify1.2s

Counts

226 → 226

Iterations

Iter	Nodes
done	2003
3	2003
2	1025
1	422
0	176

prune3.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.6b

regimes235.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	6057×	body	80	valid
451.0ms	652×	body	2560	valid
352.0ms	506×	body	1280	valid
230.0ms	285×	body	5120	valid
122.0ms	162×	body	320	valid
121.0ms	271×	body	640	valid
15.0ms	67×	body	160	valid