Details

sample58.0ms

Algorithm

intervals

Results

21.0ms	283×	body	80	nan
18.0ms	256×	body	80	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	27	28
2	44	28
3	56	28
4	74	28
5	80	28
done	80	28

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 im re) (log base))
0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 108

Calls

4 calls:

4.0ms	(* (atan2 im re) (log base))
13.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (atan2 im re) (log base))
35.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
151.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify588.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (165.0ms)

Iter	Nodes	Cost
0	194	2236
1	440	2040
2	1492	1850
done	5001	1850

prune482.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (log base))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

3.0ms

(/ (atan2 im re) (log base))

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(/ (atan2 im re) (log base))

simplify1.1s

Counts

34 → 34

Iterations

Useful iterations: 4 (337.0ms)

Iter	Nodes	Cost
0	62	380
1	103	361
2	221	337
3	620	334
4	1419	330
done	5000	330

prune108.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (log base) (atan2 im re))
0.4b	(/ 1 (/ (log base) (atan2 im re)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `associate-/r*`
16×	`log-pow`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

2 → 119

Calls

2 calls:

3.0ms	(/ (log base) (atan2 im re))
6.0ms	(/ 1 (/ (log base) (atan2 im re)))

series95.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (log base) (atan2 im re))
54.0ms	(/ 1 (/ (log base) (atan2 im re)))

simplify1.7s

Counts

125 → 125

Iterations

Useful iterations: 3 (622.0ms)

Iter	Nodes	Cost
0	162	1850
1	337	1561
2	772	1382
3	2097	1346
done	5001	1346

prune197.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (atan2 im re))
0.3b	(/ 1 (log base))
0.5b	(/ (/ 1 (log base)) (/ 1 (atan2 im re)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

550×	`times-frac`
251×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`pow1` `add-exp-log`
46×	`log-pow`
36×	`div-exp`
34×	`div-inv`
22×	`associate-/l*`
20×	`associate-/r*`
19×	`add-cbrt-cube`
10×	`cbrt-undiv` `rec-exp` `1-exp`
3×	`frac-2neg` `clear-num` `add-log-exp`
2×	`pow-flip` `inv-pow`
1×	`associate-/r/` `associate-/l/`

Counts

3 → 335

Calls

3 calls:

2.0ms	(/ 1 (atan2 im re))
2.0ms	(/ 1 (log base))
13.0ms	(/ (/ 1 (log base)) (/ 1 (atan2 im re)))

series207.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ 1 (atan2 im re))
155.0ms	(/ 1 (log base))
47.0ms	(/ (/ 1 (log base)) (/ 1 (atan2 im re)))

simplify2.5s

Counts

344 → 344

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	404	6952
1	1164	5021
2	2092	4405
3	4035	4309
done	5001	4309

prune252.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes166.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	9	6
done	9	6

end0.0ms

sample1.5s

Algorithm

intervals

Results

576.0ms	8095×	body	80	nan
571.0ms	8000×	body	80	valid