Details

sample107.0ms

Algorithm

intervals

Results

46.0ms	256×	body	80	valid
38.0ms	274×	body	80	nan

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	1130
6	438
5	190
4	132
3	86
2	48
1	31
0	18

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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:

6.0ms

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

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

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

simplify1.6s

Counts

37 → 37

Iterations

Iter	Nodes
done	5001
4	1860
3	649
2	274
1	111
0	65

prune198.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

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×	`expm1-log1p-u` `associate-/r*` `log-pow`
3×	`insert-posit16` `log1p-expm1-u` `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:

1.0ms	(log1p (/ (atan2 im re) (log base)))
0.0ms	(expm1 (log1p (/ (atan2 im re) (log base))))
9.0ms	(/ (atan2 im re) (log base))

series227.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(log1p (/ (atan2 im re) (log base)))
83.0ms	(expm1 (log1p (/ (atan2 im re) (log base))))
53.0ms	(/ (atan2 im re) (log base))

simplify2.3s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
4	1979
3	702
2	332
1	150
0	92

prune334.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

1.0ms	(expm1 (log1p (log1p (/ (atan2 im re) (log base)))))
1.0ms	(log1p (/ (atan2 im re) (log base)))
1.0ms	(expm1 (expm1 (log1p (log1p (/ (atan2 im re) (log base))))))
12.0ms	(/ (atan2 im re) (log base))

series299.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(expm1 (log1p (log1p (/ (atan2 im re) (log base)))))
70.0ms	(log1p (/ (atan2 im re) (log base)))
88.0ms	(expm1 (expm1 (log1p (log1p (/ (atan2 im re) (log base))))))
36.0ms	(/ (atan2 im re) (log base))

simplify2.4s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
4	1965
3	685
2	342
1	164
0	104

prune428.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`times-frac`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`associate-r`
15×	`add-exp-log`
12×	`pow1`
9×	`add-cbrt-cube`
7×	`log-pow`
4×	`associate-/r*` `div-exp` `prod-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`expm1-log1p-u` `cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

2 → 80

Calls

2 calls:

30.0ms	(* (atan2 im re) (/ 1 (log base)))
9.0ms	(/ 1 (log base))

series257.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(* (atan2 im re) (/ 1 (log base)))
212.0ms	(/ 1 (log base))

simplify3.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
4	2508
3	1112
2	609
1	225
0	106

prune205.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes418.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
0	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.1s	8083×	body	80	nan