Details

sample111.0ms

Algorithm

intervals

Results

52.0ms	245×	body	80	nan
41.0ms	256×	body	80	valid

simplify1.7m

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.4b	(/ (log (hypot re im)) (log base))

rewrite16.0ms

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:

5.0ms	(hypot re im)
10.0ms	(/ (log (hypot re im)) (log base))

series238.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(hypot re im)
172.0ms	(/ (log (hypot re im)) (log base))

simplify916.0ms

Counts

56 → 56

Iterations

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

prune328.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.4b	(/ (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (log base))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
88×	`log-pow`
68×	`times-frac`
48×	`sqrt-pow1` `pow1/2`
47×	`add-sqr-sqrt`
35×	`*-un-lft-identity` `add-cube-cbrt`
30×	`pow-prod-up`
18×	`pow-prod-down` `pow-sqr` `sqrt-prod`
17×	`associate-/l*`
8×	`add-cbrt-cube` `swap-sqr` `add-exp-log`
6×	`pow2` `pow-plus` `associate-r` `associate-l`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`hypot-udef`
1×	`cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `sqrt-unprod` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 178

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
32.0ms	(/ (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (log base))
19.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(hypot re im)
89.0ms	(hypot re im)
152.0ms	(/ (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (log base))
78.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify9.7s

Counts

190 → 190

Iterations

Iter	Nodes
4	6167
3	1553
2	639
1	317
0	177

prune653.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

21.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
2.0ms	(cbrt (sqrt (hypot re im)))
2.0ms	(cbrt (sqrt (hypot re im)))
2.0ms	(cbrt (sqrt (hypot re im)))

series722.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im))))
193.0ms	(cbrt (sqrt (hypot re im)))
151.0ms	(cbrt (sqrt (hypot re im)))
201.0ms	(cbrt (sqrt (hypot re im)))

simplify1.1s

Counts

122 → 122

Iterations

Iter	Nodes
4	2394
3	1011
2	427
1	185
0	95

prune579.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(/ 1 (log base))
0.3b	(* (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (/ 1 (log base)))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
45×	`pow1`
31×	`*-un-lft-identity`
30×	`add-cube-cbrt`
26×	`times-frac`
23×	`associate-l`
22×	`associate-r`
21×	`log-pow`
19×	`add-exp-log`
18×	`sqrt-prod`
16×	`sqrt-pow1` `pow1/2`
13×	`add-cbrt-cube`
10×	`pow-prod-up`
8×	`swap-sqr`
7×	`pow-prod-down` `unswap-sqr`
6×	`pow-sqr`
5×	`prod-exp`
4×	`expm1-log1p-u` `associate-/r*` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-unprod` `associate-/l*`
2×	`pow2` `cbrt-undiv` `rec-exp` `pow-plus` `1-exp` `*-commutative` `div-inv`
1×	`hypot-udef` `clear-num` `rem-square-sqrt` `frac-2neg` `sqrt-unprod` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow`

Counts

4 → 157

Calls

4 calls:

0.0ms	(hypot re im)
9.0ms	(/ 1 (log base))
52.0ms	(* (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (/ 1 (log base)))
24.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(hypot re im)
209.0ms	(/ 1 (log base))
159.0ms	(* (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (/ 1 (log base)))
79.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify2.7s

Counts

169 → 169

Iterations

Iter	Nodes
3	2159
2	914
1	347
0	173

prune725.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes481.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	14
1	14
0	12

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.6s	8000×	body	80	valid
2.2s	7955×	body	80	nan