Details

sample126.0ms

Algorithm

intervals

Results

60.0ms	304×	body	80	nan
33.0ms	256×	body	80	valid

simplify74.0ms

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
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))
0.6b	(fma (log base) (log base) (* 0.0 0.0))

rewrite36.0ms

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)
24.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
10.0ms	(* (log base) (atan2 im re))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series700.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(hypot re im)
218.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
57.0ms	(* (log base) (atan2 im re))
352.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
3	2337
2	824
1	307
0	137

prune599.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

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:

7.0ms

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

series54.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

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

simplify4.0s

Counts

36 → 36

Iterations

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

prune178.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

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

series238.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(* (atan2 im re) (/ 1 (log base)))
195.0ms	(/ 1 (log base))

simplify3.5s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	2158
3	991
2	557
1	220
0	104

prune352.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 im re) (cbrt (/ 1 (* (log base) (* (log base) (log base))))))
0.3b	(* (log base) (* (log base) (log base)))
0.6b	(* (log base) (log base))
0.7b	(cbrt (/ 1 (* (log base) (* (log base) (log base)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
28×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
15×	`cbrt-prod` `distribute-rgt-in` `distribute-lft-in` `associate-r`
13×	`add-exp-log`
12×	`add-cbrt-cube`
11×	`associate-l`
7×	`log-pow`
6×	`times-frac` `swap-sqr` `pow-prod-up`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow2` `cbrt-div` `pow-plus` `pow-sqr` `div-inv`
1×	`pow1/3` `cube-unmult` `associate-*r/`

Counts

4 → 124

Calls

4 calls:

18.0ms	(* (atan2 im re) (cbrt (/ 1 (* (log base) (* (log base) (log base))))))
17.0ms	(* (log base) (* (log base) (log base)))
8.0ms	(* (log base) (log base))
23.0ms	(cbrt (/ 1 (* (log base) (* (log base) (log base)))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (atan2 im re) (cbrt (/ 1 (* (log base) (* (log base) (log base))))))
237.0ms	(* (log base) (* (log base) (log base)))
199.0ms	(* (log base) (log base))
219.0ms	(cbrt (/ 1 (* (log base) (* (log base) (log base)))))

simplify2.0s

Counts

136 → 136

Iterations

Iter	Nodes
done	5090
3	2675
2	1110
1	374
0	164

prune644.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes352.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	6
0	6

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.5s	8039×	body	80	nan