Details

sample104.0ms

Algorithm

intervals

Results

28.0ms	186×	body	80	valid
24.0ms	26×	body	2560	valid
15.0ms	19×	body	1280	valid
14.0ms	13×	body	5120	valid
5.0ms	9×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify44.0ms

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: 39.8b

localize41.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (sqrt (+ (* re re) (* im im))) re)
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

45.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (+ (* re re) (* im im)))

series155.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
72.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

35 → 35

Iterations

Iter	Nodes
done	2008
4	2008
3	837
2	357
1	145
0	61

prune243.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.8b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.8b	(sqrt (+ (* re re) (* im im)))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite125.0ms

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:

72.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
26.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
10.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (+ (* re re) (* im im)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
81.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))
57.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts

140 → 140

Iterations

Iter	Nodes
done	2002
4	2002
3	1762
2	660
1	295
0	136

prune835.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.7b

localize60.0ms

Local error

Found 4 expressions with local error:

29.8b	(sqrt (+ (* re re) (* im im)))
29.8b	(sqrt (+ (* re re) (* im im)))
29.8b	(sqrt (+ (* re re) (* im im)))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite54.0ms

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)))
12.0ms	(sqrt (+ (* re re) (* im im)))
18.0ms	(sqrt (+ (* re re) (* im im)))
11.0ms	(sqrt (+ (* re re) (* im im)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (+ (* re re) (* im im)))
58.0ms	(sqrt (+ (* re re) (* im im)))
49.0ms	(sqrt (+ (* re re) (* im im)))
55.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	2019
5	2019
4	995
3	435
2	196
1	92
0	39

prune728.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.7b

localize100.0ms

Local error

Found 4 expressions with local error:

30.7b	(cbrt (+ (* re re) (* im im)))
30.7b	(cbrt (+ (* re re) (* im im)))
30.7b	(cbrt (+ (* re re) (* im im)))
30.7b	(cbrt (+ (* re re) (* im im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `flip3-+` `add-cbrt-cube` `pow1/3` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

8.0ms	(cbrt (+ (* re re) (* im im)))
8.0ms	(cbrt (+ (* re re) (* im im)))
16.0ms	(cbrt (+ (* re re) (* im im)))
8.0ms	(cbrt (+ (* re re) (* im im)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt (+ (* re re) (* im im)))
118.0ms	(cbrt (+ (* re re) (* im im)))
158.0ms	(cbrt (+ (* re re) (* im im)))
139.0ms	(cbrt (+ (* re re) (* im im)))

simplify1.2s

Counts

68 → 68

Iterations

Iter	Nodes
done	2000
4	2000
3	1029
2	311
1	124
0	52

prune759.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 16.7b

regimes1.0s

Accuracy

57.6% (8.2b remaining)

Error of 26.3b against oracle of 18.1b and baseline of 37.5b

bsearch183.0ms

Steps

Iters	Range		Point
9	1.5170350880269351e+122	2.839867871307593e+130	3.6193449042408916e+129
9	-9.144585154688466e-290	-5.409551245546668e-297	-5.481265975678271e-297

simplify12.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.0s	6032×	body	80	valid
811.0ms	513×	body	1280	valid
636.0ms	680×	body	2560	valid
299.0ms	278×	body	5120	valid
134.0ms	259×	body	640	valid
95.0ms	160×	body	320	valid
20.0ms	78×	body	160	valid