Details

sample84.0ms

Algorithm

intervals

Results

38.0ms	228×	body	80	nan
24.0ms	256×	body	80	valid

simplify45.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
5	80
4	74
3	56
2	44
1	27
0	18

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 im re) (log base))
0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `div-sub` `div-exp` `pow-sqr` `pow-prod-up` `div-inv` `flip--`

Counts

4 → 108

Calls

4 calls:

7.0ms	(* (atan2 im re) (log base))
24.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
8.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (atan2 im re) (log base))
57.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
162.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	2939
1	508
0	194

prune935.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

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×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

4.0ms

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

series54.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

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

simplify1.2s

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
3	1363
2	299
1	108
0	62

prune203.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

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×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `add-log-exp`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

2 → 119

Calls

2 calls:

10.0ms	(/ 1 (/ (log base) (atan2 im re)))
7.0ms	(/ (log base) (atan2 im re))

series126.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(/ 1 (/ (log base) (atan2 im re)))
51.0ms	(/ (log base) (atan2 im re))

simplify1.5s

Counts

125 → 125

Iterations

Iter	Nodes
done	5001
2	1889
1	386
0	162

prune621.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `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 → 74

Calls

2 calls:

7.0ms	(/ 1 (log base))
22.0ms	(* (atan2 im re) (/ 1 (log base)))

series266.0ms

Counts

2 → 6

Calls

2 calls:

215.0ms	(/ 1 (log base))
51.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify3.9s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	2180
1	221
0	100

prune253.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.0b

regimes397.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	6
0	6

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	7699×	body	80	nan