Details

sample53.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
17.0ms	238×	body	80	nan

simplify42.0ms

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: 33.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.6b	(* (log base) (log base))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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:

12.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (atan2 im re) (log base))
4.0ms	(* (log base) (log base))
3.0ms	(sqrt (+ (* re re) (* im im)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
28.0ms	(* (atan2 im re) (log base))
152.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify710.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (209.0ms)

Iter	Nodes	Cost
0	194	2236
1	440	2040
2	1400	1850
done	5000	1850

prune458.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/r*`
9×	`pow1`
8×	`log-pow`
4×	`neg-mul-1`
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 → 63

Calls

1 calls:

4.0ms

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

series46.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

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

simplify2.4s

Counts

66 → 66

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	106	887
1	184	841
2	387	815
3	939	807
4	2002	807
done	5000	804

prune166.0ms

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	(/ -1 (log base))
0.3b	(* (atan2 im re) (/ -1 (log base)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow`
4×	`associate-/r*`
3×	`associate-l` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 66

Calls

2 calls:

2.0ms	(/ -1 (log base))
11.0ms	(* (atan2 im re) (/ -1 (log base)))

series208.0ms

Counts

2 → 6

Calls

2 calls:

165.0ms	(/ -1 (log base))
43.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify2.3s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	99	713
1	204	644
2	644	595
3	2335	578
done	5000	578

prune186.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ -1 (pow (log base) 3))
0.3b	(* (atan2 im re) (cbrt (/ -1 (pow (log base) 3))))
0.6b	(cbrt (/ -1 (pow (log base) 3)))
0.8b	(pow (log base) 3)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

130×	`times-frac`
99×	`add-sqr-sqrt`
97×	`cbrt-prod`
84×	`add-cube-cbrt` `*-un-lft-identity`
49×	`associate-r`
45×	`unpow-prod-down` `cube-prod`
29×	`pow1`
22×	`log-pow`
14×	`associate-/r*`
12×	`add-exp-log` `sqr-pow`
11×	`cube-mult` `unpow3`
8×	`add-cbrt-cube`
6×	`unswap-sqr`
4×	`add-log-exp`
3×	`pow-unpow` `div-exp` `associate-l` `div-inv` `associate-/l*`
2×	`pow-to-exp` `cbrt-div` `pow-exp`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `pow1/3` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 223

Calls

4 calls:

5.0ms	(/ -1 (pow (log base) 3))
27.0ms	(* (atan2 im re) (cbrt (/ -1 (pow (log base) 3))))
4.0ms	(cbrt (/ -1 (pow (log base) 3)))
2.0ms	(pow (log base) 3)

series627.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ -1 (pow (log base) 3))
78.0ms	(* (atan2 im re) (cbrt (/ -1 (pow (log base) 3))))
186.0ms	(cbrt (/ -1 (pow (log base) 3)))
169.0ms	(pow (log base) 3)

simplify765.0ms

Counts

235 → 235

Iterations

Useful iterations: 2 (222.0ms)

Iter	Nodes	Cost
0	236	3119
1	423	2617
2	1272	2504
done	5001	2504

prune472.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0b

regimes225.0ms

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: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	10	8
done	10	8

end0.0ms

sample1.5s

Algorithm

intervals

Results

563.0ms	7982×	body	80	nan
559.0ms	8000×	body	80	valid