Details

sample58.0ms

Algorithm

intervals

Results

19.0ms	224×	body	80	nan
18.0ms	256×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	16
1	52	16
2	68	16
3	88	16
4	102	16
5	106	16
6	106	16
done	106	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize19.0ms

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)))
0.6b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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--` `hypot-def` `div-inv`

Counts

4 → 117

Calls

4 calls:

8.0ms	(* (atan2 im re) (log base))
31.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (atan2 im re) (log base))
41.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
154.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify58.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	466	1254
1	1924	1122
2	5002	1081
done	5002	1081

prune417.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (/ 1 base))
0.3b	(/ (atan2 im re) (log (/ 1 base)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

27×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`log-pow`
13×	`log-prod`
12×	`pow1`
9×	`add-exp-log`
6×	`associate-/r*`
5×	`pow-flip` `inv-pow`
4×	`rem-log-exp` `add-cbrt-cube`
3×	`div-exp` `associate-/l*`
2×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `log-div` `rec-exp` `frac-2neg` `1-exp` `log-rec` `clear-num`

Counts

2 → 72

Calls

2 calls:

3.0ms	(log (/ 1 base))
7.0ms	(/ (atan2 im re) (log (/ 1 base)))

series157.0ms

Counts

2 → 6

Calls

2 calls:

117.0ms	(log (/ 1 base))
40.0ms	(/ (atan2 im re) (log (/ 1 base)))

simplify103.0ms

Counts

78 → 78

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	201	450
1	518	418
2	1456	402
3	3870	389
4	5001	389
done	5001	389

prune165.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (/ 1 base))
0.2b	(/ 1 (/ (log (/ 1 base)) (atan2 im re)))
0.3b	(/ (log (/ 1 base)) (atan2 im re))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
84×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`log-pow`
38×	`pow1`
25×	`associate-/r*`
21×	`add-exp-log`
18×	`pow-flip` `inv-pow`
13×	`log-prod`
10×	`div-exp` `add-cbrt-cube`
9×	`associate-/l*`
7×	`div-inv`
4×	`cbrt-undiv` `rem-log-exp`
3×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `frac-2neg` `log-rec` `clear-num`
1×	`div-sub` `distribute-frac-neg` `associate-/r/`

Counts

3 → 188

Calls

3 calls:

3.0ms	(log (/ 1 base))
13.0ms	(/ 1 (/ (log (/ 1 base)) (atan2 im re)))
13.0ms	(/ (log (/ 1 base)) (atan2 im re))

series211.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(log (/ 1 base))
54.0ms	(/ 1 (/ (log (/ 1 base)) (atan2 im re)))
43.0ms	(/ (log (/ 1 base)) (atan2 im re))

simplify55.0ms

Counts

197 → 197

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	501	1610
1	2007	1420
2	5001	1268
done	5001	1268

prune457.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`prod-exp`
5×	`cbrt-unprod`
4×	`div-exp` `associate-/r*` `log-pow`
3×	`associate-r` `pow-prod-down` `associate-/l*`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `1-exp` `associate-*l/` `log1p-expm1-u` `add-log-exp`
1×	`distribute-lft-neg-out` `pow-flip` `frac-2neg` `mul-1-neg` `associate-r/` `associate-l` `clear-num` `un-div-inv` `-commutative` `div-inv` `inv-pow`

Counts

2 → 64

Calls

2 calls:

5.0ms	(/ 1 (log base))
34.0ms	(* (* -1 (/ 1 (log base))) (atan2 im re))

series212.0ms

Counts

2 → 6

Calls

2 calls:

151.0ms	(/ 1 (log base))
60.0ms	(* (* -1 (/ 1 (log base))) (atan2 im re))

simplify88.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	242	357
1	1093	297
2	3946	272
3	5001	272
done	5001	272

prune106.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes287.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	13
1	26	13
2	26	13
done	26	13

end0.0ms

sample1.6s

Algorithm

intervals

Results

569.0ms	8000×	body	80	valid
558.0ms	7823×	body	80	nan