Details

sample109.0ms

Algorithm

intervals

Results

37.0ms	277×	body	80	nan
35.0ms	256×	body	80	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	18	28
1	27	21
2	33	21
done	33	21

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize63.0ms

Local error

Found 3 expressions with local error:

0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.4b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.6b	(fma (log base) (log base) (* 0.0 0.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
5.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series879.0ms

Counts

3 → 9

Calls

3 calls:

183.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
253.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
443.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify3.7s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.8s)

Iter	Nodes	Cost
0	99	1324
1	179	1303
2	413	1133
3	1237	1088
4	4994	1079
done	5000	1079

prune406.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (hypot (log base) 0.0))
0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.4b	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
0.4b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

5.0ms	(/ 1 (hypot (log base) 0.0))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
27.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
10.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

496.0ms	(/ 1 (hypot (log base) 0.0))
146.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
475.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
191.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))

simplify3.5s

Counts

142 → 142

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	185	3303
1	419	3105
2	1218	2729
3	4200	2714
done	5000	2675

prune698.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (hypot (log base) 0.0))
0.3b	(/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))
0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.4b	(* (/ 1 (hypot (log base) 0.0)) (/ 1 (/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

121×	`times-frac`
109×	`add-sqr-sqrt`
93×	`add-exp-log`
73×	`*-un-lft-identity`
62×	`add-cube-cbrt`
45×	`div-exp`
44×	`associate-r`
29×	`add-cbrt-cube`
28×	`prod-exp`
16×	`rec-exp` `1-exp`
15×	`unswap-sqr`
13×	`associate-l`
11×	`cbrt-undiv`
9×	`pow1`
7×	`div-inv`
6×	`associate-/r` `cbrt-unprod` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `pow-prod-down` `inv-pow`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `associate-l/` `associate-/r/` `un-div-inv` `*-commutative` `fma-udef`

Counts

4 → 195

Calls

4 calls:

5.0ms	(/ 1 (hypot (log base) 0.0))
5.0ms	(/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
64.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ 1 (/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

595.0ms	(/ 1 (hypot (log base) 0.0))
541.0ms	(/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))
127.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
568.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ 1 (/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))))

simplify3.5s

Counts

207 → 207

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	298	5665
1	739	5133
2	1611	4615
3	4423	4441
done	5000	4353

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 3 expressions with local error:

0.4b

(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

0.4b

(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))

0.4b

(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (hypot (log base) 0.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

1.0ms

(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

10.0ms

(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))

23.0ms

(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (hypot (log base) 0.0))

series677.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms

(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

254.0ms

(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))

265.0ms

(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (hypot (log base) 0.0))

simplify2.3s

Counts

120 → 120

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	182	3809
1	368	3738
2	789	3462
3	2220	3382
done	5001	3283

prune681.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

regimes461.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	29
1	22	28
done	22	28

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.5s	8045×	body	80	nan