Details

sample62.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
18.0ms	238×	body	80	nan

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

rewrite4.0ms

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)
2.0ms	(/ (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 (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series597.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot re im)
148.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
116.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
282.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.8s

Counts

71 → 71

Iterations

Useful iterations: 4 (853.0ms)

Iter	Nodes	Cost
0	111	1384
1	196	1361
2	428	1185
3	1163	1140
4	3875	1131
done	5000	1131

prune350.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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))
0.4b	(* (/ 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))

rewrite23.0ms

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:

2.0ms	(/ 1 (hypot (log base) 0.0))
2.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
14.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (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))

series993.0ms

Counts

4 → 12

Calls

4 calls:

349.0ms	(/ 1 (hypot (log base) 0.0))
162.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
369.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
112.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

simplify2.9s

Counts

142 → 142

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	185	3303
1	442	3105
2	1227	2729
3	4646	2714
done	5001	2714

prune511.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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	(* (/ 1 (hypot (log base) 0.0)) (/ 1 (/ (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))

rewrite49.0ms

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:

2.0ms	(/ 1 (hypot (log base) 0.0))
2.0ms	(/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))
35.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ 1 (/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

549.0ms	(/ 1 (hypot (log base) 0.0))
391.0ms	(/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))
363.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ 1 (/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))))
109.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

simplify2.8s

Counts

207 → 207

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	298	5665
1	842	5133
2	1620	4615
3	4591	4448
done	5000	4419

prune675.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize15.0ms

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot re im)
2.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
6.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (hypot (log base) 0.0))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

series486.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
152.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
184.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (hypot (log base) 0.0))
105.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

simplify1.7s

Counts

133 → 133

Iterations

Useful iterations: 3 (670.0ms)

Iter	Nodes	Cost
0	194	3869
1	392	3796
2	885	3514
3	2477	3434
done	5000	3434

prune461.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes227.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	14	22
done	14	22

end0.0ms

sample1.6s

Algorithm

intervals

Results

596.0ms	7982×	body	80	nan
586.0ms	8000×	body	80	valid