Details

sample185.0ms

Algorithm

intervals

Results

92.0ms	256×	body	80	valid
62.0ms	207×	body	80	nan

simplify5.9s

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

prune12.0ms

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

rewrite17.0ms

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)
14.0ms	(/ (log (hypot re im)) (log base))

series180.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(hypot re im)
122.0ms	(/ (log (hypot re im)) (log base))

simplify3.3s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
4	1929
3	662
2	305
1	140
0	85

prune350.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

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)))

rewrite142.0ms

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)
102.0ms	(/ (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (log base))
27.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(hypot re im)
73.0ms	(hypot re im)
179.0ms	(/ (log (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (log base))
68.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify1.6s

Counts

190 → 190

Iterations

Iter	Nodes
done	5000
3	1438
2	588
1	326
0	177

prune758.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

3227×	`add-sqr-sqrt`
3156×	`sqrt-prod`
2752×	`sqrt-pow1`
2225×	`pow1`
1482×	`pow-prod-up`
1376×	`pow1/2`
1179×	`unswap-sqr`
1143×	`swap-sqr`
940×	`log-pow`
636×	`times-frac`
622×	`pow-sqr`
436×	`pow-prod-down`
249×	`*-un-lft-identity`
245×	`add-cube-cbrt`
159×	`associate-/l*`
115×	`associate-l`
113×	`associate-r`
110×	`pow-plus`
80×	`pow2`
51×	`*-commutative`
22×	`add-cbrt-cube` `add-exp-log`
10×	`prod-exp` `cbrt-unprod`
7×	`sqrt-unprod`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-square-sqrt`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 2050

Calls

4 calls:

942.0ms	(/ (log (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))) (log base))
272.0ms	(* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))
26.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
28.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (log (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))) (log base))
83.0ms	(* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))
114.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
118.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

simplify2.3s

Counts

2062 → 2062

Iterations

Iter	Nodes
done	5000
1	1901
0	729

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

3156×	`sqrt-prod`
3080×	`add-sqr-sqrt`
1182×	`unswap-sqr`
1143×	`swap-sqr`
960×	`sqrt-pow1`
727×	`pow1`
506×	`pow-prod-up`
480×	`pow1/2`
274×	`associate-l`
214×	`pow-sqr`
160×	`log-pow`
153×	`pow-prod-down`
129×	`associate-r`
97×	`*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`*-commutative`
38×	`pow-plus`
29×	`add-exp-log`
28×	`pow2`
25×	`add-cbrt-cube`
14×	`times-frac` `prod-exp`
12×	`cbrt-unprod`
10×	`associate-*r/`
7×	`sqrt-unprod`
4×	`expm1-log1p-u` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`rem-square-sqrt` `un-div-inv`
2×	`clear-num` `div-exp`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `1-exp` `div-inv`

Counts

4 → 1445

Calls

4 calls:

528.0ms	(* (log (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))) (/ 1 (log base)))
313.0ms	(* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))
25.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
32.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

series482.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (log (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))) (/ 1 (log base)))
77.0ms	(* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))
133.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
131.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

simplify2.3s

Counts

1457 → 1457

Iterations

Iter	Nodes
done	5001
2	2493
1	1163
0	385

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes308.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.5s	7974×	body	80	nan
2.2s	8000×	body	80	valid