Details

sample159.0ms

Algorithm

intervals

Results

76.0ms	256×	body	80	valid
56.0ms	233×	body	80	nan

simplify1.8m

Counts

1 → 1

Iterations

Iter	Nodes
9	22032
8	1831
7	568
6	176
5	71
4	67
3	47
2	32
1	26
0	18

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.3b	(/ (log (hypot re im)) (log base))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`times-frac`
12×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
10×	`log-pow`
4×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `hypot-udef` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 50

Calls

2 calls:

0.0ms	(hypot re im)
13.0ms	(/ (log (hypot re im)) (log base))

series219.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(hypot re im)
151.0ms	(/ (log (hypot re im)) (log base))

simplify908.0ms

Counts

56 → 56

Iterations

Iter	Nodes
4	2137
3	665
2	302
1	139
0	85

prune571.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

9.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series705.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
153.0ms	(cbrt (hypot re im))
188.0ms	(cbrt (hypot re im))
151.0ms	(cbrt (hypot re im))

simplify968.0ms

Counts

97 → 97

Iterations

Iter	Nodes
4	2176
3	960
2	424
1	165
0	80

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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))
0.6b	(cbrt (hypot re im))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series610.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (hypot re im))
164.0ms	(cbrt (hypot re im))
136.0ms	(cbrt (hypot re im))
134.0ms	(cbrt (hypot re im))

simplify929.0ms

Counts

68 → 68

Iterations

Iter	Nodes
5	2050
4	793
3	349
2	135
1	65
0	37

prune860.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

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))
5.0b	(pow (hypot re im) 1/3)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unpow-prod-down` `pow1/3`
1×	`pow-to-exp` `hypot-udef` `pow-pow` `unpow1/3` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
2.0ms	(pow (hypot re im) 1/3)

series672.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (hypot re im))
173.0ms	(cbrt (hypot re im))
162.0ms	(cbrt (hypot re im))
173.0ms	(pow (hypot re im) 1/3)

simplify3.8s

Counts

76 → 76

Iterations

Iter	Nodes
5	5824
4	1956
3	845
2	315
1	127
0	63

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes401.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	16
1	16
0	13

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.6s	8000×	body	80	valid
2.3s	8341×	body	80	nan