Details

sample111.0ms

Algorithm

intervals

Results

30.0ms	264×	body	80	nan
29.0ms	256×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	33
2	33
1	27
0	18

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.4b	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
0.6b	(* (log base) (log base))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
17×	`pow1`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `associate-/l`
1×	`pow2` `cbrt-undiv` `hypot-udef` `clear-num` `frac-2neg` `pow-plus` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
8.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
16.0ms	(* (log base) (log base))

series940.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot re im)
201.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
418.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
270.0ms	(* (log base) (log base))

simplify1.1s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	1569
1	306
0	148

prune685.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot 0.0 (log base)))
0.3b	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
0.3b	(/ (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot 0.0 (log base))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.6b	(* (log base) (log base))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
97×	`add-sqr-sqrt` `*-un-lft-identity`
95×	`add-cube-cbrt`
42×	`sqrt-prod`
17×	`pow1`
16×	`associate-/l*`
13×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`clear-num` `frac-2neg`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 191

Calls

4 calls:

4.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot 0.0 (log base)))
0.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
15.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot 0.0 (log base))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
9.0ms	(* (log base) (log base))

series861.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot 0.0 (log base)))
126.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
329.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot 0.0 (log base))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
227.0ms	(* (log base) (log base))

simplify1.5s

Counts

203 → 203

Iterations

Iter	Nodes
done	5000
2	2973
1	621
0	288

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize45.0ms

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

rewrite44.0ms

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×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 131

Calls

4 calls:

6.0ms	(/ 1 (hypot (log base) 0.0))
5.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot 0.0 (log base)))
0.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
28.0ms	(* (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot 0.0 (log base))) (/ 1 (hypot (log base) 0.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

426.0ms	(/ 1 (hypot (log base) 0.0))
186.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot 0.0 (log base)))
128.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
334.0ms	(* (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot 0.0 (log base))) (/ 1 (hypot (log base) 0.0)))

simplify2.2s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	2937
1	485
0	199

prune974.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (log base) (log base))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
15×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`cbrt-prod`
6×	`log-prod` `add-cbrt-cube` `swap-sqr` `add-exp-log` `log-pow`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow1/3`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

8.0ms	(* (log base) (log base))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series602.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(* (log base) (log base))
139.0ms	(cbrt (hypot re im))
116.0ms	(cbrt (hypot re im))
126.0ms	(cbrt (hypot re im))

simplify1.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5002
2	1206
1	199
0	89

prune600.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes568.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	16

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.5s	8087×	body	80	nan