Details

sample105.0ms

Algorithm

intervals

Results

37.0ms	268×	body	80	nan
34.0ms	256×	body	80	valid

simplify176.0ms

Counts

1 → 1

Iterations

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize67.0ms

Local error

Found 3 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

43.0ms	(/ (- (* (log base) (atan2 im re)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
17.0ms	(* (log base) (atan2 im re))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series993.0ms

Counts

3 → 9

Calls

3 calls:

265.0ms	(/ (- (* (log base) (atan2 im re)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
71.0ms	(* (log base) (atan2 im re))
657.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify4.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5004
3	2834
2	803
1	291
0	126

prune943.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

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:

13.0ms

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

series67.0ms

Counts

1 → 3

Calls

1 calls:

66.0ms

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

simplify6.9s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
5	4876
4	1808
3	658
2	273
1	110
0	64

prune392.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite60.0ms

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×	`div-exp` `prod-exp` `associate-/r*`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `1-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 78

Calls

2 calls:

13.0ms	(/ 1 (log base))
41.0ms	(* (atan2 im re) (/ 1 (log base)))

series415.0ms

Counts

2 → 6

Calls

2 calls:

349.0ms	(/ 1 (log base))
65.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify5.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	2192
3	1307
2	650
1	222
0	104

prune567.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `associate-/r*`
16×	`log-pow`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

2 → 123

Calls

2 calls:

25.0ms	(/ 1 (/ (log base) (atan2 im re)))
23.0ms	(/ (log base) (atan2 im re))

series196.0ms

Counts

2 → 6

Calls

2 calls:

110.0ms	(/ 1 (/ (log base) (atan2 im re)))
86.0ms	(/ (log base) (atan2 im re))

simplify4.6s

Counts

129 → 129

Iterations

Iter	Nodes
done	5367
3	2856
2	1079
1	382
0	166

prune649.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes722.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	8

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.6s	8060×	body	80	nan
1.7s	8000×	body	80	valid