Details

sample40.0ms

Algorithm

intervals

Results

10.0ms	203×	body	80	valid
6.0ms	21×	body	2560	valid
2.0ms	11×	body	1280	valid
2.0ms	8×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	24
2	24
1	22
0	12

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize31.0ms

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)))

rewrite129.0ms

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:

49.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
57.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
21.0ms	(sqrt (+ (* re re) (* im im)))

series402.0ms

Counts

3 → 9

Calls

3 calls:

260.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
82.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
60.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.0s

Counts

52 → 52

Iterations

Iter	Nodes
done	5002
3	2107
2	668
1	246
0	102

prune650.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.1b

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)))

rewrite288.0ms

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:

62.0ms	(sqrt (+ (sqrt (+ (* re re) (* im im))) re))
152.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
58.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
13.0ms	(sqrt (+ (* re re) (* im im)))

series706.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(sqrt (+ (sqrt (+ (* re re) (* im im))) re))
325.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
98.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify6.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5002
3	3611
2	1031
1	357
0	147

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.8b

localize70.0ms

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)))

rewrite196.0ms

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:

90.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
65.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
13.0ms	(sqrt (+ (* re re) (* im im)))
15.0ms	(sqrt (+ (* re re) (* im im)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (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)
88.0ms	(sqrt (+ (* re re) (* im im)))
91.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.5s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
3	1751
2	661
1	295
0	136

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.8b

localize280.0ms

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)))

rewrite94.0ms

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:

12.0ms	(sqrt (+ (* re re) (* im im)))
21.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
23.0ms	(sqrt (+ (* re re) (* im im)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ (* re re) (* im im)))
55.0ms	(sqrt (+ (* re re) (* im im)))
61.0ms	(sqrt (+ (* re re) (* im im)))
64.0ms	(sqrt (+ (* re re) (* im im)))

simplify6.7s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
5	3240
4	991
3	433
2	196
1	92
0	39

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 15.8b

regimes1.5s

Accuracy

56.8% (9.2b remaining)

Error of 26.7b against oracle of 17.5b and baseline of 38.8b

bsearch94.0ms

Steps

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

simplify27.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	5997×	body	80	valid
302.0ms	717×	body	2560	valid
182.0ms	295×	body	5120	valid
146.0ms	480×	body	1280	valid
77.0ms	301×	body	640	valid
26.0ms	136×	body	320	valid
9.0ms	74×	body	160	valid