Details

sample120.0ms

Algorithm

intervals

Results

35.0ms	241×	body	80	nan
35.0ms	256×	body	80	valid

simplify236.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	91
5	91
4	87
3	67
2	51
1	31
0	18

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize62.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (- (* (log base) (atan2 im re)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.4b	(* (log base) (atan2 im re))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
4×	`associate-l`
3×	`expm1-log1p-u` `associate-/r` `associate-r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `flip--` `unswap-sqr`

Counts

3 → 66

Calls

3 calls:

48.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
15.0ms	(* (log base) (atan2 im re))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.0s

Counts

3 → 9

Calls

3 calls:

385.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
101.0ms	(* (log base) (atan2 im re))
522.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify4.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	2399
2	817
1	293
0	128

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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:

8.0ms

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

series70.0ms

Counts

1 → 3

Calls

1 calls:

70.0ms

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

simplify6.4s

Counts

37 → 37

Iterations

Iter	Nodes
done	5000
4	1869
3	661
2	276
1	111
0	65

prune586.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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))

rewrite13.0ms

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:

1.0ms	(log1p (expm1 (/ (atan2 im re) (log base))))
2.0ms	(expm1 (/ (atan2 im re) (log base)))
8.0ms	(/ (atan2 im re) (log base))

series461.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(log1p (expm1 (/ (atan2 im re) (log base))))
166.0ms	(expm1 (/ (atan2 im re) (log base)))
122.0ms	(/ (atan2 im re) (log base))

simplify6.6s

Counts

67 → 67

Iterations

Iter	Nodes
done	5019
4	2648
3	744
2	351
1	152
0	91

prune958.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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:

2.0ms	(expm1 (* (atan2 im re) (/ 1 (log base))))
2.0ms	(log1p (expm1 (* (atan2 im re) (/ 1 (log base)))))
13.0ms	(/ 1 (log base))
27.0ms	(* (atan2 im re) (/ 1 (log base)))

series836.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(expm1 (* (atan2 im re) (/ 1 (log base))))
184.0ms	(log1p (expm1 (* (atan2 im re) (/ 1 (log base)))))
327.0ms	(/ 1 (log base))
111.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify6.0s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
4	2370
3	1334
2	700
1	267
0	133

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes1.3s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
1.5s	7906×	body	80	nan