Details

sample89.0ms

Algorithm

intervals

Results

38.0ms	228×	body	80	nan
27.0ms	256×	body	80	valid

simplify65.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `hypot-udef` `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

4 → 73

Calls

4 calls:

0.0ms	(hypot re im)
12.0ms	(* (log base) (atan2 im re))
21.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series774.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(hypot re im)
57.0ms	(* (log base) (atan2 im re))
222.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
422.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.0s

Counts

85 → 85

Iterations

Iter	Nodes
done	5002
3	2505
2	826
1	307
0	137

prune703.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

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` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

4.0ms

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

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

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

simplify3.9s

Counts

36 → 36

Iterations

Iter	Nodes
done	5000
5	4930
4	1906
3	668
2	273
1	110
0	64

prune256.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
60×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
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` `clear-num` `frac-2neg` `1-exp` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

2 → 123

Calls

2 calls:

11.0ms	(/ 1 (/ (log base) (atan2 im re)))
8.0ms	(/ (log base) (atan2 im re))

series114.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ 1 (/ (log base) (atan2 im re)))
52.0ms	(/ (log base) (atan2 im re))

simplify2.1s

Counts

129 → 129

Iterations

Iter	Nodes
done	5096
3	2916
2	1076
1	382
0	166

prune389.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

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` `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 → 78

Calls

2 calls:

4.0ms	(/ 1 (log base))
13.0ms	(* (atan2 im re) (/ 1 (log base)))

series236.0ms

Counts

2 → 6

Calls

2 calls:

196.0ms	(/ 1 (log base))
40.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify2.8s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	2472
3	1555
2	763
1	222
0	104

prune248.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes458.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.5s	7699×	body	80	nan
1.4s	8000×	body	80	valid