Details

sample78.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
24.0ms	244×	body	80	nan

simplify40.0ms

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)))

rewrite30.0ms

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:

13.0ms	(/ (- (* (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)))

series46.0ms

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))
16.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify479.0ms

Counts

120 → 120

Iterations

Useful iterations: done (476.0ms)

Iter	Nodes	Cost
0	195	2250
1	444	2117
2	1510	1906
done	5001	1849

prune247.0ms

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))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

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

simplify1.8s

Counts

34 → 34

Iterations

Useful iterations: 4 (173.0ms)

Iter	Nodes	Cost
0	65	384
1	108	365
2	258	338
3	634	332
4	1614	330
5	4651	330
done	5000	330

prune76.0ms

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)))

rewrite14.0ms

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

series30.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(/ 1 (log base))
12.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify885.0ms

Counts

80 → 80

Iterations

Useful iterations: 4 (468.0ms)

Iter	Nodes	Cost
0	102	771
1	214	646
2	679	525
3	1458	513
4	2884	509
done	5001	509

prune88.0ms

Filtered

35 candidates to 80 candidates (-128.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	79	12	91

Merged error: 0.0b

Counts

91 → 12

localize8.0ms

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))

series26.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify1.1s

Counts

125 → 125

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	164	1858
1	347	1639
2	1111	1471
3	2965	1350
done	5000	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	123	2	125
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	124	13	137

Merged error: 0.0b

Counts

137 → 13

regimes372.0ms

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

sample2.3s

Algorithm

intervals

Results

834.0ms	8000×	body	80	valid
782.0ms	7896×	body	80	nan

Details

sample78.0ms

simplify40.0ms

prune5.0ms

localize20.0ms

rewrite30.0ms

series46.0ms

simplify479.0ms

prune247.0ms

localize6.0ms

rewrite4.0ms

series12.0ms

simplify1.8s

prune76.0ms

localize8.0ms

rewrite14.0ms

series30.0ms

simplify885.0ms

prune88.0ms

localize8.0ms

rewrite17.0ms

series26.0ms

simplify1.1s

prune61.0ms

regimes372.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling