Details

sample132.0ms

Algorithm

intervals

Results

56.0ms	256×	body	80	valid
35.0ms	232×	body	80	nan

simplify105.0ms

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	78	28
done	78	28

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize46.0ms

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))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite83.0ms

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:

9.0ms	(* (atan2 im re) (log base))
38.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
18.0ms	(* (log base) (log base))
15.0ms	(sqrt (+ (* re re) (* im im)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (atan2 im re) (log base))
48.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
187.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.7s

Counts

120 → 120

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	194	2236
1	441	2040
2	1394	1850
3	4937	1817
done	5001	1817

prune512.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

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:

11.0ms

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

series61.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

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

simplify2.9s

Counts

34 → 34

Iterations

Useful iterations: 4 (268.0ms)

Iter	Nodes	Cost
0	62	380
1	103	361
2	210	337
3	388	334
4	672	330
5	2100	330
done	5000	330

prune155.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

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:

11.0ms	(/ 1 (/ (log base) (atan2 im re)))
8.0ms	(/ (log base) (atan2 im re))

series123.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(/ 1 (/ (log base) (atan2 im re)))
48.0ms	(/ (log base) (atan2 im re))

simplify1.9s

Counts

125 → 125

Iterations

Useful iterations: 3 (627.0ms)

Iter	Nodes	Cost
0	162	1850
1	321	1561
2	621	1382
3	1617	1346
done	5000	1346

prune247.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite46.0ms

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×	`div-exp` `prod-exp` `associate-/r*`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 74

Calls

2 calls:

11.0ms	(/ 1 (log base))
22.0ms	(* (atan2 im re) (/ 1 (log base)))

series291.0ms

Counts

2 → 6

Calls

2 calls:

248.0ms	(/ 1 (log base))
42.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify4.1s

Counts

80 → 80

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	100	761
1	197	590
2	429	522
3	869	516
4	1646	510
done	5000	510

prune111.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes302.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
1.3s	8016×	body	80	nan