Details

sample22.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

56.0ms	(+ (* re re) (* im im))
61.0ms	(sqrt (+ (* re re) (* im im)))

series99.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+ (* re re) (* im im))
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
3	1579
2	382
1	132
0	52

prune133.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (* re re) (* im im))))
0.2b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
31.0b	(cbrt (+ (* re re) (* im im)))
31.0b	(cbrt (+ (* re re) (* im im)))

rewrite345.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
34×	`cbrt-prod`
24×	`sqrt-prod`
20×	`add-sqr-sqrt` `distribute-lft-out`
19×	`associate-l`
14×	`associate-r`
12×	`add-cube-cbrt`
8×	`cbrt-div` `swap-sqr`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `sqrt-div` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow1/3` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

59.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
171.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
58.0ms	(cbrt (+ (* re re) (* im im)))
52.0ms	(cbrt (+ (* re re) (* im im)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
171.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
115.0ms	(cbrt (+ (* re re) (* im im)))
132.0ms	(cbrt (+ (* re re) (* im im)))

simplify1.9s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
3	2713
2	739
1	289
0	133

prune478.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.1b

localize41.0ms

Local error

Found 4 expressions with local error:

31.0b	(cbrt (+ (* re re) (* im im)))
31.0b	(cbrt (+ (* re re) (* im im)))
31.0b	(cbrt (+ (* re re) (* im im)))
31.0b	(cbrt (+ (* re re) (* im im)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
32×	`cbrt-prod`
20×	`distribute-lft-out`
16×	`associate-l`
8×	`add-sqr-sqrt` `cbrt-div` `swap-sqr` `add-cube-cbrt`
4×	`pow1` `flip3-+` `add-cbrt-cube` `pow1/3` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

57.0ms	(cbrt (+ (* re re) (* im im)))
59.0ms	(cbrt (+ (* re re) (* im im)))
58.0ms	(cbrt (+ (* re re) (* im im)))
36.0ms	(cbrt (+ (* re re) (* im im)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(cbrt (+ (* re re) (* im im)))
161.0ms	(cbrt (+ (* re re) (* im im)))
126.0ms	(cbrt (+ (* re re) (* im im)))
152.0ms	(cbrt (+ (* re re) (* im im)))

simplify2.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5037
4	3809
3	1014
2	313
1	126
0	54

prune499.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.1b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.1b

regimes434.0ms

Accuracy

57.7% (9.0b remaining)

Error of 16.6b against oracle of 7.5b and baseline of 28.9b

bsearch108.0ms

Steps

Iters	Range		Point
9	1.4356436329954285e+137	2.3935951588787148e+142	5.887500437435469e+139
10	-3.706207899435069e+161	-2.779942061402865e+151	-1.2743190345131582e+154

simplify4.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample831.0ms

Algorithm

intervals

Results

642.0ms

8000×

body

valid