Details

sample90.0ms

Algorithm

intervals

Results

36.0ms	256×	body	80	valid
25.0ms	264×	body	80	nan

simplify59.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (* (log base) (atan2 im re)) (* (log (sqrt (+ (* im im) (* re re)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log base) (atan2 im re))
0.6b	(* (log base) (log base))
28.8b	(sqrt (+ (* im im) (* re re)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`pow1` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`associate-l`
7×	`associate-r` `log-pow`
6×	`log-prod` `swap-sqr`
4×	`add-log-exp`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `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 → 102

Calls

4 calls:

32.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (sqrt (+ (* im im) (* re re)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log base) (atan2 im re))
11.0ms	(* (log base) (log base))
12.0ms	(sqrt (+ (* im im) (* re re)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (sqrt (+ (* im im) (* re re)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
54.0ms	(* (log base) (atan2 im re))
237.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* im im) (* re re)))

simplify1.6s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	2658
1	485
0	185

prune881.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (+ 0 (log base)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
15×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`distribute-lft-out`
5×	`pow1` `associate-/r*`
4×	`log-pow`
3×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 37

Calls

1 calls:

14.0ms

(/ (atan2 im re) (+ 0 (log base)))

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

(/ (atan2 im re) (+ 0 (log base)))

simplify296.0ms

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
2	653
1	157
0	74

prune195.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

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))
17.0ms	(* (atan2 im re) (/ 1 (log base)))

series296.0ms

Counts

2 → 6

Calls

2 calls:

245.0ms	(/ 1 (log base))
51.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify3.6s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	2180
1	221
0	100

prune281.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (atan2 im re) (- (* (log base) (log base))))
0.4b	(* (/ (atan2 im re) (- (* (log base) (log base)))) (- 0 (log base)))
0.6b	(* (log base) (log base))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
37×	`times-frac`
36×	`*-un-lft-identity`
31×	`add-cube-cbrt`
26×	`associate-l`
19×	`pow1`
12×	`add-cbrt-cube` `add-exp-log`
10×	`associate-r`
7×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `log-pow`
6×	`log-prod` `associate-/r*` `swap-sqr`
5×	`distribute-rgt-in` `distribute-lft-in`
3×	`prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `sub-neg` `flip3--` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `flip--` `distribute-lft-out--`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `associate-*l/` `pow-sqr` `pow-prod-up` `distribute-rgt-neg-out` `difference-of-squares` `sub0-neg`

Counts

3 → 128

Calls

3 calls:

5.0ms	(/ (atan2 im re) (- (* (log base) (log base))))
41.0ms	(* (/ (atan2 im re) (- (* (log base) (log base)))) (- 0 (log base)))
8.0ms	(* (log base) (log base))

series270.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ (atan2 im re) (- (* (log base) (log base))))
42.0ms	(* (/ (atan2 im re) (- (* (log base) (log base)))) (- 0 (log base)))
167.0ms	(* (log base) (log base))

simplify3.0s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	4803
1	542
0	201

prune667.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes411.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
2	10
1	9
0	8

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.1s	8087×	body	80	nan