Details

sample31.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

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

series124.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(+ (* re re) (* im im))
75.0ms	(sqrt (+ (* re re) (* im im)))

simplify461.0ms

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
2	770
1	142
0	48

prune159.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
28.4b	(sqrt (+ (* re re) (* im im)))
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite67.0ms

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`
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 → 124

Calls

4 calls:

6.0ms	(+ (* re re) (* im im))
45.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* re re) (* im im))
42.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
49.0ms	(sqrt (+ (* re re) (* im im)))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	1649
1	292
0	121

prune466.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (fabs (cbrt (+ (pow im 2) (pow re 2))))) (sqrt (sqrt (+ (pow im 2) (pow re 2)))))
28.4b	(sqrt (+ (pow im 2) (pow re 2)))
29.4b	(cbrt (+ (* re re) (* im im)))
29.4b	(cbrt (+ (pow im 2) (pow re 2)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-prod`
25×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`associate-r`
9×	`pow1`
8×	`cbrt-prod`
6×	`unpow-prod-down` `add-cbrt-cube` `sqrt-div` `associate-l` `add-exp-log` `distribute-lft-out` `unswap-sqr`
4×	`cbrt-div` `flip3-+` `flip-+` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`pow1/3` `associate-*r/`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 84

Calls

4 calls:

55.0ms	(* (sqrt (fabs (cbrt (+ (pow im 2) (pow re 2))))) (sqrt (sqrt (+ (pow im 2) (pow re 2)))))
19.0ms	(sqrt (+ (pow im 2) (pow re 2)))
8.0ms	(cbrt (+ (* re re) (* im im)))
10.0ms	(cbrt (+ (pow im 2) (pow re 2)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (sqrt (fabs (cbrt (+ (pow im 2) (pow re 2))))) (sqrt (sqrt (+ (pow im 2) (pow re 2)))))
40.0ms	(sqrt (+ (pow im 2) (pow re 2)))
120.0ms	(cbrt (+ (* re re) (* im im)))
96.0ms	(cbrt (+ (pow im 2) (pow re 2)))

simplify801.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1629
1	386
0	171

prune785.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 9.0b

localize4.0ms

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: 9.0b

regimes470.0ms

Accuracy

56.3% (10.4b remaining)

Error of 18.0b against oracle of 7.6b and baseline of 31.5b

bsearch73.0ms

Steps

Iters	Range		Point
10	1.770057870633885e+84	1.1610867076317608e+95	1.1493803764036757e+95
9	-7.317563595848081e+70	-3.473568020675254e+63	-1.9401195934627838e+70

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample651.0ms

Algorithm

intervals

Results

382.0ms

8000×

body

valid