Details

sample26.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize15.0ms

Local error

Found 1 expressions with local error:

29.7b

(sqrt (+ (* re re) (* im im)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 16

Calls

1 calls:

9.0ms

(sqrt (+ (* re re) (* im im)))

series63.0ms

Counts

1 → 3

Calls

1 calls:

63.0ms

(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

19 → 19

Iterations

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

prune60.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

6.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
9.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
54.0ms	(sqrt (+ (* re re) (* im im)))
45.0ms	(sqrt (+ (* re re) (* im im)))
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify995.0ms

Counts

77 → 77

Iterations

Iter	Nodes
done	2004
4	2004
3	1040
2	341
1	149
0	72

prune379.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.9b

localize28.0ms

Local error

Found 4 expressions with local error:

4.1b	(exp (log (cbrt (sqrt (+ (* re re) (* im im))))))
29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`sqrt-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-sum`
8×	`pow1` `sqrt-div`
6×	`cbrt-prod`
5×	`exp-prod`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`log-div` `cbrt-div` `exp-diff` `log-pow`
1×	`pow1/3` `rem-exp-log`

Counts

4 → 73

Calls

4 calls:

8.0ms	(exp (log (cbrt (sqrt (+ (* re re) (* im im))))))
7.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(exp (log (cbrt (sqrt (+ (* re re) (* im im))))))
41.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify957.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
4	2000
3	1144
2	409
1	199
0	113

prune381.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.9b

localize67.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

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)))
13.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))
47.0ms	(sqrt (+ (* re re) (* im im)))
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify891.0ms

Counts

76 → 76

Iterations

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

prune503.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.9b

regimes383.0ms

Accuracy

56.9% (9.3b remaining)

Error of 17.2b against oracle of 7.9b and baseline of 29.5b

bsearch159.0ms

Steps

Iters	Range		Point
8	7.938065894163254e+92	5.466900983039234e+96	5.360456255819538e+96
8	2.682856457515952e-293	3.682879132878819e-290	4.660720867938078e-293
7	-1.5942858179205256e-248	-4.44103357617797e-250	-1.9219302233631307e-249
10	-3.5676395954738344e+156	-2.7527531001535463e+137	-1.6423327785059521e+153

simplify6.0ms

Iterations

Iter	Nodes
done	20
1	20
0	19

end0.0ms

sample798.0ms

Algorithm

intervals

Results

615.0ms

8000×

body

valid