Details

sample105.0ms

Algorithm

intervals

Results

46.0ms	232×	body	80	nan
30.0ms	256×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

localize19.0ms

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))
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))

series1.4s

Counts

4 → 12

Calls

4 calls:

58.0ms	(hypot re im)
166.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
257.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
902.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.5s

Counts

71 → 71

Iterations

Useful iterations: done (1.5s)

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

prune555.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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))

rewrite38.0ms

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))
25.0ms	(/ (/ (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))))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

231.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
369.0ms	(/ (/ (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))))
145.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
446.0ms	(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

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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/` `un-div-inv` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 131

Calls

4 calls:

5.0ms	(/ 1 (hypot 0.0 (log base)))
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))
26.0ms	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (/ 1 (hypot 0.0 (log base))))

series1.2s

Counts

4 → 12

Calls

4 calls:

475.0ms	(/ 1 (hypot 0.0 (log base)))
244.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
160.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
290.0ms	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (/ 1 (hypot 0.0 (log base))))

simplify2.7s

Counts

143 → 143

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	199	3267
1	448	3072
2	1143	2688
3	3594	2681
done	5000	2680

prune723.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize25.0ms

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)

rewrite31.0ms

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:

17.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3)))
2.0ms	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
3.0ms	(pow (log base) 2)
3.0ms	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

series1.1s

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3)))
297.0ms	(cbrt (pow (fma 0.0 0.0 (pow (log base) 2)) 3))
177.0ms	(pow (log base) 2)
371.0ms	(pow (fma 0.0 0.0 (pow (log base) 2)) 3)

simplify909.0ms

Counts

158 → 158

Iterations

Useful iterations: done (901.0ms)

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

prune731.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes393.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.3s	8016×	body	80	nan
1.3s	8000×	body	80	valid