Details

sample129.0ms

Algorithm

intervals

Results

54.0ms	239×	body	80	nan
36.0ms	256×	body	80	valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize49.0ms

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)) (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))

rewrite14.0ms

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:

1.0ms	(hypot re im)
10.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (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))

series916.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(hypot re im)
250.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
158.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
444.0ms	(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	197	1361
2	492	1185
3	1852	1140
done	5001	1135

prune998.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

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)) (hypot (log base) 0.0))
0.4b	(/ (/ (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))))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite62.0ms

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:

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))
35.0ms	(/ (/ (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 base) (log base) (* 0.0 0.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

149.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
212.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
348.0ms	(/ (/ (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))))
526.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.4s

Counts

175 → 175

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	259	6925
1	559	6630
2	2383	5592
done	5000	5391

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize54.0ms

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))
0.4b	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (cbrt (pow (hypot 0.0 (log base)) (* 2 3)))))
0.4b	(cbrt (pow (hypot 0.0 (log base)) (* 2 3)))
1.1b	(pow (hypot 0.0 (log base)) (* 2 3))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

304×	`times-frac`
169×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
140×	`sqrt-prod`
105×	`cbrt-prod`
48×	`unpow-prod-down`
16×	`associate-/r` `div-inv` `associate-/l` `sqr-pow`
12×	`add-exp-log`
11×	`add-cbrt-cube`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `pow-unpow` `hypot-udef` `pow-pow` `pow1/3` `pow-exp` `sqrt-pow2` `associate-/l/`

Counts

4 → 276

Calls

4 calls:

9.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
24.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (cbrt (pow (hypot 0.0 (log base)) (* 2 3)))))
11.0ms	(cbrt (pow (hypot 0.0 (log base)) (* 2 3)))
3.0ms	(pow (hypot 0.0 (log base)) (* 2 3))

series1.7s

Counts

4 → 12

Calls

4 calls:

246.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
327.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (cbrt (pow (hypot 0.0 (log base)) (* 2 3)))))
515.0ms	(cbrt (pow (hypot 0.0 (log base)) (* 2 3)))
580.0ms	(pow (hypot 0.0 (log base)) (* 2 3))

simplify2.4s

Counts

288 → 288

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	429	13100
1	947	11757
2	4689	11467
done	5000	11312

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (hypot (log base) 0.0))
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)) (hypot (log base) 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)))

rewrite67.0ms

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:

10.0ms	(/ 1 (hypot (log base) 0.0))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
9.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
41.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

485.0ms	(/ 1 (hypot (log base) 0.0))
144.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
219.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
483.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

simplify2.3s

Counts

142 → 142

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	185	3303
1	473	3179
2	3051	2737
done	5000	2735

prune806.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes412.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.7s	8139×	body	80	nan
1.4s	8000×	body	80	valid