Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	194×	body	80	valid
4.0ms	23×	body	2560	valid
2.0ms	14×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	9×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8
done	24	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
31.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
45.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Counts

49 → 49

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	244	351
1	743	325
2	2278	315
3	5001	312
done	5001	312

prune151.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite105.0ms

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:

51.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
30.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
48.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Counts

136 → 136

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950
done	5001	950

prune289.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.9b

localize21.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(cbrt (+ (* re re) (* im im)))
30.6b	(cbrt (+ (* re re) (* im im)))
30.6b	(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

8.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))
7.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify51.0ms

Counts

66 → 66

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	141	466
1	440	436
2	1469	430
3	5002	429
done	5002	429

prune366.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.9b

localize26.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (+ (* re re) (* im im)))
30.6b	(cbrt (+ (* re re) (* im im)))
30.6b	(cbrt (+ (* re re) (* im im)))
30.6b	(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

10.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify51.0ms

Counts

66 → 66

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	141	466
1	440	436
2	1469	430
3	5002	429
done	5002	429

prune397.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 16.9b

regimes230.0ms

Accuracy

49.7% (10.8b remaining)

Error of 28.2b against oracle of 17.4b and baseline of 38.8b

bsearch140.0ms

Steps

Iters	Range	Point
8	5.820219195236088e+119	5.264749266612397e+122	4.3167714370166035e+122
10	7.495911143049393e-219	4.3617670924590225e-206	1.5163028629072722e-218
7	-3.357300134911745e-38	-3.2345611474486164e-40	-3.282394346843421e-40

Iters

Range

Point

5.820219195236088e+119

5.264749266612397e+122

4.3167714370166035e+122

7.495911143049393e-219

4.3617670924590225e-206

1.5163028629072722e-218

-3.357300134911745e-38

-3.2345611474486164e-40

-3.282394346843421e-40

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	48
1	68	48
2	68	48
done	68	48

end0.0ms

sample708.0ms

Algorithm

intervals

Results

196.0ms	6025×	body	80	valid
129.0ms	664×	body	2560	valid
74.0ms	492×	body	1280	valid
64.0ms	287×	body	5120	valid
33.0ms	280×	body	640	valid
14.0ms	158×	body	320	valid
6.0ms	94×	body	160	valid