Details

sample82.0ms

Algorithm

intervals

Results

31.0ms	270×	body	80	nan
30.0ms	256×	body	80	valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5529
8	3678
7	666
6	215
5	80
4	75
3	51
2	36
1	26
0	18

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

16×	`times-frac`
13×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
11×	`log-pow`
5×	`add-exp-log`
4×	`associate-/r` `add-cbrt-cube` `associate-/l`
3×	`log-prod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `div-inv`

Counts

2 → 54

Calls

2 calls:

1.0ms	(log (hypot re im))
9.0ms	(/ (log (hypot re im)) (log base))

series218.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(log (hypot re im))
137.0ms	(/ (log (hypot re im)) (log base))

simplify3.4s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
4	1954
3	649
2	265
1	135
0	85

prune266.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`times-frac`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`add-exp-log`
16×	`associate-r`
15×	`pow1`
10×	`add-cbrt-cube`
9×	`log-pow`
4×	`associate-/r` `div-exp` `associate-l*` `prod-exp`
3×	`expm1-log1p-u` `log-prod` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `rem-log-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 96

Calls

3 calls:

2.0ms	(log (hypot re im))
6.0ms	(/ 1 (log base))
16.0ms	(* (log (hypot re im)) (/ 1 (log base)))

series396.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(log (hypot re im))
207.0ms	(/ 1 (log base))
117.0ms	(* (log (hypot re im)) (/ 1 (log base)))

simplify1.8s

Counts

105 → 105

Iterations

Iter	Nodes
done	5013
4	2959
3	1270
2	684
1	248
0	125

prune447.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt` `*-un-lft-identity`
35×	`log-pow`
34×	`pow1`
30×	`add-cube-cbrt`
26×	`times-frac` `associate-l`
19×	`add-exp-log`
16×	`associate-r`
12×	`log-prod`
11×	`add-cbrt-cube`
10×	`distribute-rgt-out`
8×	`sqrt-pow1` `pow1/2` `distribute-lft-out`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-/r*` `div-exp` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `distribute-lft1-in` `flip3-+` `1-exp` `rem-log-exp` `associate-*l/` `distribute-rgt1-in` `cbrt-unprod` `flip-+` `div-inv`
1×	`clear-num` `frac-2neg` `count-2` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 147

Calls

4 calls:

2.0ms	(log (sqrt (hypot re im)))
2.0ms	(log (sqrt (hypot re im)))
4.0ms	(/ 1 (log base))
32.0ms	(* (+ (log (sqrt (hypot re im))) (log (sqrt (hypot re im)))) (/ 1 (log base)))

series663.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(log (sqrt (hypot re im)))
111.0ms	(log (sqrt (hypot re im)))
222.0ms	(/ 1 (log base))
217.0ms	(* (+ (log (sqrt (hypot re im))) (log (sqrt (hypot re im)))) (/ 1 (log base)))

simplify2.4s

Counts

159 → 159

Iterations

Iter	Nodes
done	5000
3	4118
2	1374
1	503
0	215

prune600.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (log (cbrt (hypot re im))) (log (cbrt (hypot re im)))) (log (cbrt (hypot re im)))) (log base))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

175×	`*-un-lft-identity`
168×	`log-pow`
157×	`pow1`
128×	`times-frac`
125×	`distribute-lft-out`
75×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
55×	`distribute-lft1-in` `distribute-rgt-out`
32×	`associate-/l*`
30×	`distribute-rgt1-in`
18×	`pow1/3`
15×	`count-2`
9×	`cbrt-prod`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 223

Calls

4 calls:

98.0ms	(/ (+ (+ (log (cbrt (hypot re im))) (log (cbrt (hypot re im)))) (log (cbrt (hypot re im)))) (log base))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series600.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (+ (+ (log (cbrt (hypot re im))) (log (cbrt (hypot re im)))) (log (cbrt (hypot re im)))) (log base))
135.0ms	(cbrt (hypot re im))
143.0ms	(cbrt (hypot re im))
160.0ms	(cbrt (hypot re im))

simplify2.2s

Counts

235 → 235

Iterations

Iter	Nodes
done	5002
3	3252
2	909
1	338
0	167

prune683.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes345.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	12

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
1.2s	7673×	body	80	nan