Details

sample46.0ms

Algorithm

intervals

Results

25.0ms

256×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize45.0ms

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))
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

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:

6.0ms	(+ (* re re) (* im im))
22.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
12.0ms	(sqrt (+ (* re re) (* im im)))

series328.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* re re) (* im im))
220.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
71.0ms	(sqrt (+ (* re re) (* im im)))

simplify637.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
2	1092
1	277
0	125

prune527.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.9b

localize24.0ms

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)))
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite150.0ms

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))
80.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
32.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
9.0ms	(sqrt (+ (* re re) (* im im)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* re re) (* im im))
171.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
284.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

217 → 217

Iterations

Iter	Nodes
done	5000
2	3993
1	714
0	247

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.8b

localize32.0ms

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))))))
3.9b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite113.0ms

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:

17.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
47.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
22.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
20.0ms	(sqrt (+ (* re re) (* im im)))

series1.5s

Counts

4 → 12

Calls

4 calls:

430.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
497.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
500.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
56.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
2	3216
1	667
0	229

prune870.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 8.7b

localize43.0ms

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)))))
28.6b	(sqrt (+ (* re re) (* im im)))

rewrite188.0ms

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:

13.0ms	(+ (* re re) (* im im))
142.0ms	(* (/ (/ 1 (sqrt (log 10.0))) (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
13.0ms	(sqrt (+ (* re re) (* im im)))

series281.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (* re re) (* im im))
184.0ms	(* (/ (/ 1 (sqrt (log 10.0))) (sqrt (log 10.0))) (log (sqrt (+ (* re re) (* im im)))))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

262 → 262

Iterations

Iter	Nodes
done	5000
2	3473
1	726
0	273

prune1.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.7b

regimes1.8s

Accuracy

58.1% (10.1b remaining)

Error of 17.1b against oracle of 7.0b and baseline of 31.2b

bsearch65.0ms

Steps

Iters	Range		Point
9	3.1824451401819005e+22	2.525601364358299e+31	9.282772713307498e+30
3	-1.1611654526548658e+117	-8.48111626998625e+116	-9.850726757232305e+116

simplify4.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample1.1s

Algorithm

intervals

Results

776.0ms

8000×

body

valid