Details

sample128.0ms

Algorithm

intervals

Results

56.0ms	233×	body	80	nan
52.0ms	256×	body	80	valid

simplify1.7m

Counts

1 → 1

Iterations

Iter	Nodes
8	16015
7	1249
6	479
5	207
4	123
3	83
2	47
1	31
0	18

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
1×	`expm1-log1p-u` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 34

Calls

1 calls:

9.0ms

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

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

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

simplify808.0ms

Counts

37 → 37

Iterations

Iter	Nodes
4	2093
3	631
2	273
1	110
0	65

prune402.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
7×	`pow1`
5×	`add-cbrt-cube` `add-exp-log`
4×	`associate-/r*` `log-pow` `log1p-expm1-u`
3×	`expm1-log1p-u` `insert-posit16` `associate-/l*` `add-log-exp`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `div-exp` `log1p-expm1` `div-inv` `expm1-udef`

Counts

3 → 58

Calls

3 calls:

0.0ms	(log1p (expm1 (/ (atan2 im re) (log base))))
0.0ms	(expm1 (/ (atan2 im re) (log base)))
4.0ms	(/ (atan2 im re) (log base))

series219.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(log1p (expm1 (/ (atan2 im re) (log base))))
82.0ms	(expm1 (/ (atan2 im re) (log base)))
44.0ms	(/ (atan2 im re) (log base))

simplify998.0ms

Counts

67 → 67

Iterations

Iter	Nodes
4	2217
3	700
2	335
1	149
0	91

prune959.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (* (atan2 im re) (/ 1 (log base)))))
0.2b	(expm1 (* (atan2 im re) (/ 1 (log base))))
0.2b	(/ 1 (log base))
0.3b	(* (atan2 im re) (/ 1 (log base)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`times-frac`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`add-exp-log`
16×	`associate-r`
14×	`pow1`
11×	`add-cbrt-cube`
7×	`log-pow`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-/r*` `div-exp` `prod-exp` `insert-posit16` `add-log-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `pow-prod-down` `log1p-expm1` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow` `expm1-udef`

Counts

4 → 104

Calls

4 calls:

0.0ms	(log1p (expm1 (* (atan2 im re) (/ 1 (log base)))))
0.0ms	(expm1 (* (atan2 im re) (/ 1 (log base))))
4.0ms	(/ 1 (log base))
10.0ms	(* (atan2 im re) (/ 1 (log base)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(log1p (expm1 (* (atan2 im re) (/ 1 (log base)))))
78.0ms	(expm1 (* (atan2 im re) (/ 1 (log base))))
239.0ms	(/ 1 (log base))
53.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify10.1s

Counts

116 → 116

Iterations

Iter	Nodes
4	2849
3	1320
2	632
1	264
0	133

prune1.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 im re) (cbrt (* (/ 1 (log base)) (/ (/ 1 (log base)) (log base)))))
0.3b	(* (/ 1 (log base)) (/ (/ 1 (log base)) (log base)))
0.3b	(/ (/ 1 (log base)) (log base))
0.6b	(cbrt (* (/ 1 (log base)) (/ (/ 1 (log base)) (log base))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
166×	`add-sqr-sqrt`
128×	`*-un-lft-identity`
120×	`add-cube-cbrt`
82×	`pow1`
80×	`add-exp-log`
72×	`associate-r`
63×	`log-pow`
40×	`div-exp`
31×	`add-cbrt-cube`
21×	`prod-exp`
19×	`associate-l`
17×	`div-inv`
16×	`associate-/l*` `unswap-sqr`
12×	`cbrt-undiv`
10×	`rec-exp` `1-exp`
7×	`cbrt-unprod`
6×	`cbrt-div` `associate-*r/` `pow-div`
5×	`pow-flip` `inv-pow`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-*l/`
2×	`cbrt-prod` `cube-unmult` `pow-prod-down` `*-commutative`
1×	`clear-num` `frac-2neg` `pow1/3` `rem-cbrt-cube` `associate-/l/`

Counts

4 → 292

Calls

4 calls:

7.0ms	(* (atan2 im re) (cbrt (* (/ 1 (log base)) (/ (/ 1 (log base)) (log base)))))
40.0ms	(* (/ 1 (log base)) (/ (/ 1 (log base)) (log base)))
9.0ms	(/ (/ 1 (log base)) (log base))
8.0ms	(cbrt (* (/ 1 (log base)) (/ (/ 1 (log base)) (log base))))

series817.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (atan2 im re) (cbrt (* (/ 1 (log base)) (/ (/ 1 (log base)) (log base)))))
283.0ms	(* (/ 1 (log base)) (/ (/ 1 (log base)) (log base)))
259.0ms	(/ (/ 1 (log base)) (log base))
234.0ms	(cbrt (* (/ 1 (log base)) (/ (/ 1 (log base)) (log base))))

simplify6.2s

Counts

304 → 304

Iterations

Iter	Nodes
2	2709
1	859
0	317

prune4.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

regimes510.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
1	8
0	8

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.7s	8341×	body	80	nan
2.4s	8000×	body	80	valid