Details

sample75.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
24.0ms	244×	body	80	nan

simplify41.0ms

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

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.9b

Counts

2 → 1

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)))
0.3b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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:

14.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (atan2 im re) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
11.0ms	(* (atan2 im re) (log base))
17.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify470.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (131.0ms)

Iter	Nodes	Cost
0	195	2250
1	444	2115
2	1447	1849
done	5001	1849

prune252.0ms

Filtered

81 candidates to 120 candidates (-48.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	109	11	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Merged error: 0.1b

Counts

121 → 11

localize6.0ms

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))

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify572.0ms

Counts

34 → 34

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	65	384
1	108	364
2	234	335
3	559	330
4	1476	330
done	5000	330

prune77.0ms

Filtered

22 candidates to 34 candidates (-54.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	27	7	34
Fresh	7	3	10
Picked	0	1	1
Done	0	0	0
Total	34	11	45

Merged error: 0.0b

Counts

45 → 11

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

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:

4.0ms	(/ 1 (log base))
12.0ms	(* (atan2 im re) (/ 1 (log base)))

series31.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(/ 1 (log base))
12.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify810.0ms

Counts

80 → 80

Iterations

Useful iterations: 3 (166.0ms)

Iter	Nodes	Cost
0	102	771
1	214	633
2	617	519
3	1529	509
4	3548	509
done	5000	509

prune98.0ms

Filtered

35 candidates to 80 candidates (-128.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	78	13	91

Merged error: 0.0b

Counts

91 → 13

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

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:

7.0ms	(/ 1 (/ (log base) (atan2 im re)))
4.0ms	(/ (log base) (atan2 im re))

series27.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(/ 1 (/ (log base) (atan2 im re)))
13.0ms	(/ (log base) (atan2 im re))

simplify624.0ms

Counts

125 → 125

Iterations

Useful iterations: 3 (242.0ms)

Iter	Nodes	Cost
0	164	1858
1	347	1625
2	1060	1380
3	2793	1346
done	5001	1346

prune61.0ms

Filtered

52 candidates to 125 candidates (-140.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	10	10
Picked	1	0	1
Done	0	2	2
Total	125	13	138

Merged error: 0.0b

Counts

138 → 13

regimes377.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
done	6	6

end0.0ms

sample2.2s

Algorithm

intervals

Results

830.0ms	8000×	body	80	valid
765.0ms	7896×	body	80	nan

Details

sample75.0ms

simplify41.0ms

prune5.0ms

localize20.0ms

rewrite32.0ms

series47.0ms

simplify470.0ms

prune252.0ms

localize6.0ms

rewrite4.0ms

series13.0ms

simplify572.0ms

prune77.0ms

localize8.0ms

rewrite18.0ms

series31.0ms

simplify810.0ms

prune98.0ms

localize11.0ms

rewrite17.0ms

series27.0ms

simplify624.0ms

prune61.0ms

regimes377.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling