Details

sample71.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
25.0ms	232×	body	80	nan

simplify58.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.3b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
6.0ms	(/ (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))

series895.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(hypot re im)
144.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
234.0ms	(/ (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))

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	111	1384
1	196	1361
2	433	1185
3	1261	1140
done	5000	1131

prune576.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
0.3b	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
0.3b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

5.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
14.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
353.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
147.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
434.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.5s

Counts

175 → 175

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	259	6925
1	533	6630
2	1101	5576
3	2980	5382
done	5002	5253

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

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))
5.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
37.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

546.0ms	(/ 1 (hypot (log base) 0.0))
221.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
190.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
459.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

simplify3.3s

Counts

142 → 142

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	185	3303
1	418	3105
2	1215	2729
3	4147	2714
done	5000	2675

prune645.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3)))
0.5b	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
0.5b	(pow (log base) 2)
0.7b	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-prod`
45×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`unpow-prod-down`
18×	`cube-prod`
15×	`associate-/r*`
8×	`add-exp-log`
7×	`pow1` `sqr-pow`
6×	`cube-mult` `pow-unpow` `unpow3` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `pow-exp`
1×	`cbrt-undiv` `frac-2neg` `pow1/3` `div-exp` `clear-num` `log-pow` `rem-cbrt-cube` `div-inv` `unpow2` `rem-cube-cbrt`

Counts

4 → 146

Calls

4 calls:

18.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3)))
5.0ms	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
6.0ms	(pow (log base) 2)
6.0ms	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

series1.0s

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3)))
220.0ms	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
212.0ms	(pow (log base) 2)
395.0ms	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

simplify928.0ms

Counts

158 → 158

Iterations

Useful iterations: done (919.0ms)

Iter	Nodes	Cost
0	202	4162
1	350	3631
2	910	3211
done	5001	3098

prune612.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes325.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	17	27
done	17	27

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.8s	8000×	body	80	valid
1.6s	8016×	body	80	nan