Details

sample40.0ms

Algorithm

intervals

Results

11.0ms	197×	body	80	valid
5.0ms	18×	body	2560	valid
3.0ms	7×	body	5120	valid
3.0ms	9×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	15
1	24	15
done	24	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
24.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
57.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
17.0ms	(sqrt (+ (* re re) (* im im)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* re re) (* im im))
281.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
79.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

63 → 63

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	108	888
1	552	761
done	5000	709

prune289.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.3b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

115.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
62.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
17.0ms	(sqrt (+ (* re re) (* im im)))
26.0ms	(sqrt (+ (* re re) (* im im)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
79.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
43.0ms	(sqrt (+ (* re re) (* im im)))
69.0ms	(sqrt (+ (* re re) (* im im)))

simplify5.0s

Counts

136 → 136

Iterations

Useful iterations: done (5.0s)

Iter	Nodes	Cost
0	133	3041
done	5000	1787

prune636.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 22.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`

Counts

4 → 54

Calls

4 calls:

50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
15.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
66.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
47.0ms	(sqrt (+ (* re re) (* im im)))
69.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

66 → 66

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	59	858
1	255	738
2	1216	686
done	5000	670

prune409.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 22.3b

localize27.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

16.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (+ (* re re) (* im im)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ (* re re) (* im im)))
46.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.1s

Counts

72 → 72

Iterations

Useful iterations: 2 (166.0ms)

Iter	Nodes	Cost
0	38	852
1	170	744
2	626	680
3	2817	680
done	5000	680

prune455.0ms

Pruning

14 alts after pruning (10 fresh and 4 done)

Merged error: 22.3b

regimes1.0s

Accuracy

48.1% (9.0b remaining)

Error of 30.2b against oracle of 21.2b and baseline of 38.6b

bsearch155.0ms

Steps

Iters	Range		Point
8	9.20494146023971e+137	8.337939306029303e+141	1.3595155319523303e+138
7	-3.7885935661345695e+111	-1.9215371086303872e+109	-6.847894715956926e+109

simplify13.0ms

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	27	37
1	36	32
done	36	32

end0.0ms

sample2.1s

Algorithm

intervals

Results

719.0ms	690×	body	2560	valid
563.0ms	6004×	body	80	valid
210.0ms	474×	body	1280	valid
179.0ms	310×	body	5120	valid
74.0ms	295×	body	640	valid
27.0ms	151×	body	320	valid
13.0ms	76×	body	160	valid