Details

sample21.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7
done	11	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

29.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
8.0ms	(sqrt (+ (* re re) (* im im)))

series167.0ms

Counts

2 → 6

Calls

2 calls:

130.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify124.0ms

Counts

69 → 69

Iterations

Useful iterations: 4 (118.0ms)

Iter	Nodes	Cost
0	221	664
1	556	631
2	1309	628
3	4047	628
4	5001	627
done	5001	627

prune194.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 194

Calls

3 calls:

56.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
29.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series367.0ms

Counts

3 → 9

Calls

3 calls:

133.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
197.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Counts

203 → 203

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	613	2721
1	2483	2427
2	5002	2334
done	5002	2334

prune426.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.2b	(* (/ 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)))

rewrite84.0ms

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` `sqrt-pow2` `flip-+`

Counts

4 → 151

Calls

4 calls:

12.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
41.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
15.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series988.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
335.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
327.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Counts

163 → 163

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	558	2291
1	2343	1895
2	5002	1744
done	5002	1744

prune413.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.2b	(* (/ 1 (sqrt (log 10.0))) (* 1 (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)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
50×	`add-cube-cbrt` `log-prod` `*-un-lft-identity`
45×	`sqrt-prod`
42×	`times-frac`
40×	`distribute-rgt-in` `distribute-lft-in`
38×	`add-exp-log`
36×	`unpow-prod-down`
25×	`pow-unpow` `associate-l`
20×	`prod-exp`
18×	`pow1`
16×	`add-cbrt-cube`
7×	`1-exp` `log-pow`
6×	`div-exp` `cbrt-unprod` `sqr-pow`
4×	`add-log-exp`
3×	`rec-exp` `pow-pow` `rem-log-exp` `pow-prod-down`
2×	`cbrt-undiv` `pow-to-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `div-inv`
1×	`rem-sqrt-square` `flip3-+` `associate-r` `associate-l/` `-commutative` `sqrt-pow2` `flip-+`

Counts

4 → 174

Calls

4 calls:

14.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
70.0ms	(* (/ 1 (sqrt (log 10.0))) (* 1 (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))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

295.0ms	(log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
357.0ms	(* (/ 1 (sqrt (log 10.0))) (* 1 (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))))
332.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Counts

186 → 186

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	817	2844
1	2978	2191
2	5001	2010
done	5001	2010

prune384.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.8b

regimes774.0ms

Accuracy

57% (10.5b remaining)

Error of 17.5b against oracle of 7.0b and baseline of 31.5b

bsearch136.0ms

Steps

Iters	Range		Point
8	3.978686766170509e+64	1.2964566837885159e+67	1.2410865450670411e+67
4	7.427089056077598e-281	1.0961453402580365e-280	7.758435713562232e-281
10	-1.2708908275756568e-290	-1.1187802841012395e-302	-8.357854099413859e-296
7	-4.232272370085704e+115	-2.3541312420272248e+113	-2.552702335522332e+114

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	52
1	56	52
2	56	52
done	56	52

end0.0ms

sample521.0ms

Algorithm

intervals

Results

335.0ms

8000×

body

valid