Details

sample48.0ms

Algorithm

intervals

Results

26.0ms

256×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	10

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`associate-/r*` `sqrt-div`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 74

Calls

3 calls:

26.0ms	(+ (* re re) (* im im))
39.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
13.0ms	(sqrt (+ (* re re) (* im im)))

series295.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* re re) (* im im))
200.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
64.0ms	(sqrt (+ (* re re) (* im im)))

simplify615.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
2	1092
1	277
0	125

prune559.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
108×	`add-sqr-sqrt`
78×	`sqrt-prod`
67×	`*-un-lft-identity`
61×	`log-pow` `add-cube-cbrt`
53×	`pow1`
46×	`associate-r`
28×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
16×	`sqrt-pow1` `pow1/2`
15×	`unswap-sqr`
9×	`div-exp`
8×	`prod-exp`
7×	`associate-/r*`
6×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv`
4×	`sqrt-div` `cbrt-unprod`
3×	`flip3-+` `flip-+` `div-inv`
2×	`log-div` `rec-exp` `1-exp` `div-sub`
1×	`frac-times` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 205

Calls

4 calls:

12.0ms	(+ (* re re) (* im im))
85.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
22.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
11.0ms	(sqrt (+ (* re re) (* im im)))

series664.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* re re) (* im im))
227.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
347.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

217 → 217

Iterations

Iter	Nodes
done	5000
2	3993
1	714
0	247

prune998.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.3b	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.8b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
45×	`add-cube-cbrt`
41×	`sqrt-prod`
30×	`log-prod`
25×	`pow-unpow` `associate-l`
24×	`unpow-prod-down`
16×	`add-exp-log`
15×	`pow1`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-cbrt-cube`
8×	`log-pow`
5×	`unswap-sqr`
4×	`associate-r` `prod-exp` `add-log-exp` `sqr-pow`
3×	`pow-pow` `rem-log-exp`
2×	`pow-to-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `pow-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `flip3-+` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `sqrt-pow2`

Counts

4 → 151

Calls

4 calls:

16.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
77.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
13.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
6.0ms	(sqrt (+ (* re re) (* im im)))

series1.5s

Counts

4 → 12

Calls

4 calls:

458.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
562.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
437.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
2	3216
1	667
0	229

prune955.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ (/ 1 (sqrt (log 10.0))) (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

340×	`times-frac`
202×	`sqrt-prod`
196×	`add-sqr-sqrt`
179×	`associate-l`
162×	`*-un-lft-identity`
158×	`add-cube-cbrt`
54×	`pow1`
49×	`log-pow`
18×	`add-exp-log`
12×	`log-prod` `add-cbrt-cube` `unswap-sqr`
9×	`div-inv`
6×	`distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-r`
5×	`prod-exp` `add-log-exp`
3×	`cbrt-undiv` `cbrt-unprod`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 253

Calls

3 calls:

12.0ms	(+ (* re re) (* im im))
129.0ms	(* (/ (/ 1 (sqrt (log 10.0))) (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
6.0ms	(sqrt (+ (* re re) (* im im)))

series321.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(+ (* re re) (* im im))
209.0ms	(* (/ (/ 1 (sqrt (log 10.0))) (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

262 → 262

Iterations

Iter	Nodes
done	5000
2	3473
1	726
0	273

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.4b

regimes1.9s

Accuracy

56.9% (10.6b remaining)

Error of 17.7b against oracle of 7.1b and baseline of 31.8b

bsearch144.0ms

Steps

Iters	Range		Point
10	1.770057870633885e+84	1.1610867076317608e+95	7.747777771049568e+94
9	-7.317563595848081e+70	-3.473568020675254e+63	-2.3669509176686378e+69

simplify8.0ms

Iterations

Iter	Nodes
done	37
1	37
0	30

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8000×

body

valid