Details

sample19.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
done	7	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize9.0ms

Local error

Found 1 expressions with local error:

31.7b

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

11.0ms

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

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

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

simplify2.7s

Counts

18 → 18

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	38	213
1	91	186
2	205	170
3	444	164
4	1114	164
5	3182	164
done	5001	164

prune63.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
31.7b	(sqrt (+ (* re re) (* im im)))
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
49×	`add-sqr-sqrt`
34×	`sqrt-pow1`
28×	`pow1` `sqrt-div`
18×	`pow1/2`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
5×	`add-exp-log` `pow-prod-down` `pow-sqr` `add-cbrt-cube`
4×	`frac-times`
3×	`add-log-exp`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

3 → 113

Calls

3 calls:

61.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0ms	(sqrt (+ (* re re) (* im im)))
10.0ms	(sqrt (+ (* re re) (* im im)))

series113.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
39.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

122 → 122

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	112	2637
1	208	1598
2	531	1440
3	1449	1365
done	5000	1328

prune286.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (* re re) (* im im))))
0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
32.6b	(cbrt (+ (* re re) (* im im)))
32.6b	(cbrt (+ (* re re) (* im im)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

14.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
38.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.0ms	(cbrt (+ (* re re) (* im im)))
7.0ms	(cbrt (+ (* re re) (* im im)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (cbrt (+ (* re re) (* im im))))
152.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
123.0ms	(cbrt (+ (* re re) (* im im)))
125.0ms	(cbrt (+ (* re re) (* im im)))

simplify1.7s

Counts

86 → 86

Iterations

Useful iterations: 3 (477.0ms)

Iter	Nodes	Cost
0	126	1572
1	277	1459
2	737	1290
3	1780	1274
done	5000	1274

prune301.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 9.8b

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 9.8b

regimes315.0ms

Accuracy

57.8% (10.1b remaining)

Error of 17.9b against oracle of 7.8b and baseline of 31.8b

bsearch102.0ms

Steps

Iters	Range		Point
8	1.0656776998337841e+73	2.1069570435261278e+76	2.076008095509726e+76
8	-8.88757827843957e-288	-5.138571342544288e-291	-1.3500686547790216e-288
9	-8.553073611070034e-194	-1.0428205539953484e-198	-1.082781542809915e-198
11	-2.9940927381484837e+161	-7.137879564257508e+129	-4.391819308233852e+130

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	36
1	20	36
done	20	36

end0.0ms

sample465.0ms

Algorithm

intervals

Results

226.0ms

8000×

body

valid