Details

sample147.0ms

Algorithm

intervals

Results

63.0ms	253×	body	80	nan
42.0ms	256×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
done	23	28

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
79.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
19.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series575.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
178.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
203.0ms	(* (log base) (log base))
56.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.8s

Counts

122 → 122

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	200	2451
1	442	2259
2	1344	2035
3	4400	1998
done	5000	1992

prune624.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(pow (log base) 2)
0.5b	(* (log base) (log base))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
157×	`add-sqr-sqrt`
156×	`*-un-lft-identity`
154×	`add-cube-cbrt`
141×	`sqrt-prod`
24×	`associate-/l*`
20×	`pow1`
18×	`sqrt-div`
16×	`associate-/r/`
12×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`flip3-+` `flip-+`
8×	`div-inv`
7×	`log-pow`
6×	`log-prod` `swap-sqr` `associate-/r*`
4×	`unpow-prod-down` `associate-r` `associate-l` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `pow-unpow` `distribute-lft-in` `div-exp`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 261

Calls

4 calls:

108.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms	(pow (log base) 2)
13.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
212.0ms	(pow (log base) 2)
246.0ms	(* (log base) (log base))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

273 → 273

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	417	14712
1	881	13094
2	1921	12399
done	5001	12041

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(* (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
0.5b	(pow (log base) 2)
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`add-cube-cbrt` `associate-r`
16×	`add-exp-log`
14×	`pow1`
11×	`times-frac` `add-cbrt-cube`
9×	`associate-l`
6×	`log-prod`
5×	`prod-exp` `log-pow`
4×	`unpow-prod-down` `flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod` `cbrt-unprod`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `rec-exp` `pow-pow` `1-exp` `associate-*r/` `pow-exp` `un-div-inv` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
86.0ms	(* (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
3.0ms	(pow (log base) 2)
9.0ms	(sqrt (+ (* re re) (* im im)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
126.0ms	(* (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
216.0ms	(pow (log base) 2)
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

116 → 116

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	230	2560
1	558	2345
2	1711	2084
done	5001	2065

prune611.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im)))))
28.7b	(sqrt (+ (* re re) (* im im)))
28.7b	(sqrt (+ (* re re) (* im im)))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
20×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `sqrt-prod`
14×	`log-pow`
12×	`log-prod`
8×	`swap-sqr`
7×	`sqrt-pow1` `pow1/2`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `sqrt-div` `associate-r` `associate-l` `add-cbrt-cube`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

32.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im)))))
11.0ms	(sqrt (+ (* re re) (* im im)))
15.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im)))))
46.0ms	(sqrt (+ (* re re) (* im im)))
54.0ms	(sqrt (+ (* re re) (* im im)))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

105 → 105

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	100	1938
1	199	1717
2	493	1501
3	1022	1327
4	2594	1302
done	5000	1272

prune635.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

regimes529.0ms

Accuracy

44.9% (17.2b remaining)

Error of 17.6b against oracle of 0.4b and baseline of 31.6b

bsearch269.0ms

Steps

Iters	Range		Point
7	6.339840813053149e+121	2.3550264976555788e+123	2.0419723084508157e+122
10	-4.380668659171097e+101	-2.9418035763948187e+87	-3.181961503270048e+94

simplify33.0ms

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	44	79
1	56	77
done	56	77

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.8s	7718×	body	80	nan
1.1s	8000×	body	80	valid