Details

sample112.0ms

Algorithm

intervals

Results

41.0ms	256×	body	80	valid
38.0ms	228×	body	80	nan

simplify126.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	78
5	78
4	74
3	56
2	44
1	27
0	18

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize69.0ms

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))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-cbrt-cube` `add-exp-log`
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-+` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `div-sub` `div-exp` `pow-sqr` `pow-prod-up` `div-inv` `flip--`

Counts

4 → 108

Calls

4 calls:

14.0ms	(* (atan2 im re) (log base))
32.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* re re) (* im im)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (atan2 im re) (log base))
56.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
248.0ms	(* (log base) (log base))
52.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.1s

Counts

120 → 120

Iterations

Iter	Nodes
done	5002
2	1721
1	506
0	194

prune902.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 31

Calls

1 calls:

4.0ms

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

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

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

simplify3.6s

Counts

34 → 34

Iterations

Iter	Nodes
done	5002
4	2039
3	677
2	276
1	108
0	62

prune224.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
60×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
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` `clear-num` `frac-2neg` `1-exp` `add-log-exp`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

2 → 119

Calls

2 calls:

10.0ms	(/ 1 (/ (log base) (atan2 im re)))
9.0ms	(/ (log base) (atan2 im re))

series120.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ 1 (/ (log base) (atan2 im re)))
57.0ms	(/ (log base) (atan2 im re))

simplify1.5s

Counts

125 → 125

Iterations

Iter	Nodes
done	5010
3	2480
2	857
1	379
0	162

prune441.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 74

Calls

2 calls:

5.0ms	(/ 1 (log base))
22.0ms	(* (atan2 im re) (/ 1 (log base)))

series252.0ms

Counts

2 → 6

Calls

2 calls:

216.0ms	(/ 1 (log base))
36.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify2.8s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
4	2205
3	1317
2	680
1	218
0	100

prune204.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.0b

regimes342.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	6
0	6

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.3s	7699×	body	80	nan