Details

sample19.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	11	12
done	11	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(log (sqrt (+ (* re re) (* im im))))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
3.0ms	(log (sqrt (+ (* re re) (* im im))))
11.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
58.0ms	(log (sqrt (+ (* re re) (* im im))))
133.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

105 → 105

Iterations

Useful iterations: 3 (357.0ms)

Iter	Nodes	Cost
0	135	1680
1	265	1585
2	690	1429
3	2108	1423
done	5001	1423

prune296.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 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)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
108×	`add-sqr-sqrt`
78×	`sqrt-prod`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt` `log-pow`
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×	`+-commutative` `frac-times` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative`

Counts

4 → 205

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
43.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
12.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* re re) (* im im))
135.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
213.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

217 → 217

Iterations

Useful iterations: 2 (262.0ms)

Iter	Nodes	Cost
0	247	4621
1	645	4164
2	1794	3647
done	5000	3647

prune473.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt (+ (* re re) (* im im))))
0.3b	(/ 1 (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))))
0.6b	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
97×	`log-pow`
93×	`add-sqr-sqrt`
92×	`add-cube-cbrt` `*-un-lft-identity`
81×	`pow1`
34×	`associate-/r*`
23×	`sqrt-pow1` `pow1/2`
18×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`log-prod` `sqrt-prod` `div-inv`
4×	`cbrt-undiv` `sqrt-div` `add-log-exp`
2×	`log-div` `rec-exp` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+`
1×	`rem-sqrt-square` `pow-flip` `rem-log-exp` `associate-/r/` `inv-pow`

Counts

4 → 216

Calls

4 calls:

3.0ms	(log (sqrt (+ (* re re) (* im im))))
9.0ms	(/ 1 (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))))
7.0ms	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(log (sqrt (+ (* re re) (* im im))))
139.0ms	(/ 1 (/ (log 10.0) (log (sqrt (+ (* re re) (* im im))))))
145.0ms	(/ (log 10.0) (log (sqrt (+ (* re re) (* im im)))))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.4s

Counts

228 → 228

Iterations

Useful iterations: 4 (2.4s)

Iter	Nodes	Cost
0	250	4656
1	528	4063
2	980	3714
3	2069	3630
4	4117	3628
done	5000	3628

prune353.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.3b	(* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 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)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

156×	`sqrt-prod`
150×	`times-frac`
132×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
77×	`add-cube-cbrt`
64×	`log-pow`
61×	`pow1`
56×	`associate-l`
47×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
18×	`unswap-sqr`
16×	`sqrt-pow1` `pow1/2`
14×	`sqrt-div`
7×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`frac-times` `associate-r/` `associate-/l`
4×	`pow-prod-down` `associate-*l/` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`log-div` `flip3-+` `div-sub` `*-commutative` `flip-+`
1×	`rem-sqrt-square` `frac-2neg` `clear-num`

Counts

4 → 244

Calls

4 calls:

45.0ms	(* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
58.0ms	(* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))))
12.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series861.0ms

Counts

4 → 12

Calls

4 calls:

470.0ms	(* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
151.0ms	(* (sqrt (/ 1 (sqrt (log 10.0)))) (* (sqrt (/ 1 (sqrt (log 10.0)))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))))
204.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts

256 → 256

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	284	6214
1	661	5561
2	1868	5213
done	5000	4921

prune647.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.7b

regimes916.0ms

Accuracy

58.3% (10.3b remaining)

Error of 17.4b against oracle of 7.1b and baseline of 31.8b

bsearch102.0ms

Steps

Iters	Range		Point
7	1.8684288122828866e+141	1.487546070235645e+143	6.23122095692667e+141
8	-7.694350151096703e+119	-2.0669682865938928e+117	-4.687222610662785e+117

simplify34.0ms

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	43	80
1	66	80
2	80	78
3	94	78
4	107	78
5	119	78
6	124	78
7	129	78
done	129	78

end0.0ms

sample479.0ms

Algorithm

intervals

Results

339.0ms

8000×

body

valid