Details

sample58.0ms

Algorithm

intervals

Results

22.0ms	252×	body	80	nan
18.0ms	256×	body	80	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	28
1	31	22
2	52	22
3	68	22
4	88	22
5	100	22
6	104	22
done	104	22

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 4 expressions with local error:

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

series427.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
72.0ms	(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
32.0ms	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
277.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify545.0ms

Counts

71 → 71

Iterations

Useful iterations: done (544.0ms)

Iter	Nodes	Cost
0	105	1432
1	189	1415
2	454	1233
3	1308	1180
done	5000	1176

prune340.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (log base))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 33

Calls

1 calls:

2.0ms

(/ (atan2 im re) (log base))

series35.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(/ (atan2 im re) (log base))

simplify3.2s

Counts

36 → 36

Iterations

Useful iterations: 5 (833.0ms)

Iter	Nodes	Cost
0	64	394
1	108	375
2	246	351
3	537	348
4	1184	346
5	2712	344
done	5001	344

prune115.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(expm1 (log1p (/ (atan2 im re) (log base))))
0.2b	(log1p (/ (atan2 im re) (log base)))
0.3b	(/ (atan2 im re) (log base))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 55

Calls

3 calls:

0.0ms	(expm1 (log1p (/ (atan2 im re) (log base))))
0.0ms	(log1p (/ (atan2 im re) (log base)))
2.0ms	(/ (atan2 im re) (log base))

series149.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(expm1 (log1p (/ (atan2 im re) (log base))))
55.0ms	(log1p (/ (atan2 im re) (log base)))
36.0ms	(/ (atan2 im re) (log base))

simplify220.0ms

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	89	675
1	137	627
2	285	572
3	581	563