Details

sample59.0ms

Algorithm

intervals

Results

18.0ms	203×	body	80	valid
11.0ms	21×	body	2560	valid
5.0ms	11×	body	1280	valid
3.0ms	5×	body	5120	valid
3.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	3×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	24
2	24
1	22
0	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize46.0ms

Local error

Found 3 expressions with local error:

0.3b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`sqrt-div` `add-cube-cbrt` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `pow-prod-down` `distribute-lft-out`

Counts

3 → 43

Calls

3 calls:

27.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
40.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series407.0ms

Counts

3 → 9

Calls

3 calls:

274.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
67.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
66.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

52 → 52

Iterations

Iter	Nodes
done	5002
3	2104
2	669
1	246
0	102

prune391.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (sqrt (+ (* re re) (* im im))) re))
0.4b	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`sqrt-prod`
16×	`*-un-lft-identity`
10×	`pow1` `add-cube-cbrt`
7×	`associate-r`
6×	`add-cbrt-cube` `sqrt-div` `associate-l` `add-exp-log` `add-log-exp`
4×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `insert-posit16` `unswap-sqr`
3×	`pow-prod-down` `distribute-lft-out`
2×	`rem-sqrt-square` `associate-*r/`
1×	`+-commutative` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 80

Calls

4 calls:

53.0ms	(sqrt (+ (sqrt (+ (* re re) (* im im))) re))
125.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
36.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(sqrt (+ (sqrt (+ (* re re) (* im im))) re))
241.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
77.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5003
3	3523
2	1029
1	357
0	147

prune505.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.7b

localize30.0ms

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)
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `insert-posit16`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

100.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
69.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
16.0ms	(sqrt (+ (* re re) (* im im)))
16.0ms	(sqrt (+ (* re re) (* im im)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
91.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
63.0ms	(sqrt (+ (* re re) (* im im)))
42.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
3	1762
2	660
1	295
0	136

prune655.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.7b

localize57.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
10.0ms	(sqrt (+ (* re re) (* im im)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (+ (* re re) (* im im)))
49.0ms	(sqrt (+ (* re re) (* im im)))
45.0ms	(sqrt (+ (* re re) (* im im)))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
5	3254
4	995
3	435
2	196
1	92
0	39

prune663.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 15.7b

regimes403.0ms

Accuracy

56.9% (8.7b remaining)

Error of 26.1b against oracle of 17.4b and baseline of 37.7b

bsearch108.0ms

Steps

Iters	Range		Point
9	3.744575579279384e+78	4.277967120250836e+83	3.920451788983101e+83
4	3.190126808092148e-299	4.3928790087306694e-299	3.2277128143621017e-299

simplify7.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample2.2s

Algorithm

intervals

Results

853.0ms	717×	body	2560	valid
543.0ms	5997×	body	80	valid
246.0ms	295×	body	5120	valid
221.0ms	480×	body	1280	valid
87.0ms	301×	body	640	valid
30.0ms	136×	body	320	valid
11.0ms	74×	body	160	valid